India won the third match in a canter to seal the series 1-0 after New Zealand were dismissed for just 175 early in the second session on the fourth day at VCA Stadium.
Following their first innings failure of 193, that saw India prevail by the margin of an innings and 198 runs, the fifth heaviest innings reverse in New Zealand history.
Vettori, of course, was not the happiest of campers after his side fell over in just 51.2 overs.
"There were a lot of negatives for us but I think India showed us how to play in these conditions, and definitely with the bat," Vettori said.
"We lost the game with the bat, unfortunately.
"Any time you lose it is a surrender and we are disappointed with our performance.
"We knew we had to be positive this morning but I think a couple of the dismissals were a little over positive."
The top order's double failure -- New Zealand had collapsed to 51 for five on the opening day here -- irrepairably hurt the team's ability to stay in the game.
"In this part of the world first innings runs keep you in the game," Vettori said.
"The overall performance was poor compared to what we did in the first two test matches.
"We were exceptional (in drawn tests at Ahmedabad and Hyderabad) because we grinded it out and made sure we put enough runs on the board."
The New Zealanders will spend the next two days at Nagpur before heading to Guwahati for the opening game in a five-match one-day series which starts on Sunday.
India in control after Dravid's 191
There's little call for liferafts in this land locked city so New Zealand will have to construct their own as they battle for survival in the third cricket test here against India.
Nothing but choppy seas confront the tourists after the hosts underlined their No 1 test nation status on the third day at VCA Stadium.
India were in control at stumps after declaring at 566 for eight in their first innings, which left the New Zealanders facing a deficit of 373 runs, the equal seventh highest in their history.
In 11 overs before the close, they had time to lose opener Tim McIntosh for eight, trapped leg before wicket playing back to offspinner Harbhajan Singh before Brendon McCullum, on 15, and nightwatchman Gareth Hopkins, on one, took them to 24 for one.
Rahul Dravid, who stroked a regal 191, and skipper MS Dhoni, 98, made life as difficult as possible for the visitors today with an Indian record equalling stand of 193 for the sixth wicket after New Zealand snapped up three quick wickets this morning, including that of the legendary Sachin Tendulkar, who became the first test wicket for new cap Andy McKay.
Dravid, who turns 38 in January, resumed on 69 this morning before methodically navigating his way to his second century of the series and the 31st of an illustrious career before setting his sights on double century No 6.
It was well within his grasp, too, when he got himself out, trying to hit part-time spinner Kane Williamson out of the ground only to be well caught by Martin Guptill at long on.
Dravid was furious with himself but should later soften the self admonishment after a most disciplined and authoritative innings.
While he lived up to his nickname of "The Wall" with a resolute display of patience interspersed with some trademark drives and cuts over 573 minutes, Dhoni took the attack to the tourists after surviving a life on 42 when Tim McIntosh could not hold on to a difficult chance at deep mid off.
Dhoni went to his 50 off just 62 balls then accelerated as he planted left-arm fast bowler McKay over his head for six before slamming a straight drive for four in the same over.
He hooked, he pulled, he drove and he cut with a freedom affording him by India's position of strength and seemed destined for his fifth test hundred until he spooned a soft catch back at spinner Daniel Vettori shortly after tea after facing 156 balls.
Subservient throughout the opening two days, the tourists had their best session of the match to claim three wickets this morning.
After another early start as officials strive to make up for time lost on the first day, New Zealand finally imposed themselves, however briefly, as Tendulkar, VVS Laxman and an out-of-sorts Suresh Raina were all sent packing in the space of 12 overs at a cost of 32 runs.
The Indians had resumed at a powerful 292 for two and all eyes were on Tendulkar as the best batsman of his generation took guard on 57, a mere 43 runs away from becoming to first player to register 50 test centuries.
After a lean series Tendulkar showed signs yesterday that he was back in the groove and it was assumed by all and sundry that he would duly deliver a thick slice of history today.
But someone forgot to tell that to the New Zealanders and in particular McKay, who marked his debut test with the most prized scalp in world cricket.
In just the second over of the day Tendulkar edged McKay's first ball to the third man boundary and two balls later McKay got some extra bounce to a delivery angled across the living legend, who again offered an edge, this time into the gloves of wicketkeeper Gareth Hopkins.
It was just the start the tourists so desperately needed with the second new ball, which Chris Martin made full use of to produce a peach of a ball to send back middle order rock Laxman.
Laxman was comfortable in reaching 12 before Martin uprooted his off stump with a ball which swung in, leaving the Indian all at sea.
Raina then continued his miserable series, making just three before a defensive prod forward to Vettori's first ball of the day resulted in an inside edge on to his pad then into the hands of substitute fielder BJ Watling under the helmet.
Raina's soft dismissal left him with the princely sum of 26 runs from four innings against the New Zealanders.
BLACKCAPS battling on day two
The BLACKCAPS are battling in the third cricket Test against India after a disappointing first innings performance with the bat handed the hosts the upperhand and India were happy to accept it on the second day on the series decider at VCA Stadium, although New Zealand's concerns ran deeper than that due to a back injury to Brendon McCullum.
McCullum overcame the discomfort to score a battling 40 in his side's inadequate first innings of 193 after they slumped to 51 for five yesterday.
India were in no mood to sympathise and cantered into the lead as they reached a threatening 292 for two in response by stumps.
They benefited from a robust 74 from Virender Sehwag and a resolute 78 from fellow opener Gautam Gambhir before Rahul Dravid hit 69 not out and Sachin Tendulkar emerged after a quiet series to contribute 54 in an unbroken stand of precisely 100 for the third wicket.
The New Zealanders settled for containment and frustration in the final session, employing ring fields to Tendulkar and Dravid as just 22 runs came in the first hour before the tempo changed after drinks.
The two 37-year-old veterans were content to bide their time before Dravid duly raised the 60th test half-century of his long career with a cut through point off spinner Daniel Vettori after 173 minutes.
One run earlier he got a genuine outside edge to left-arm fast bowler Andy McKay but the ball died just short of a fully stretched wicketkeeper Gareth Hopkins.
Tendulkar, seeking to become the first man to score 50 test centuries, was peppered by short deliveries at his body by young seamer Tim Southee, and the team scallywag had the cheek to hit the veteran twice on the body and once even tried to stare down the great man.
He was too wise for all that, slowly building his momentum as half-century 59 was ticked off from 117 balls in 143 minutes.
India were just one run short of New Zealand's total when they lost their second wicket of the afternoon session when Gambhir, who spent 191 minutes in the middle, weakly steered an unthreatening ball from Southee to Ross Taylor at wide slip.
Sehwag had been his irrepressible self, taking the long handle to fast bowlers Chris Martin and Southee, who were both hit out of the attack after four overs each.
He reached 50 for the fourth time in five innings in this series then targeted Vettori in the second session.
Sehwag had lifted his series aggregate to 398 runs before the New Zealand captain had the last laugh, holding on to a solidly hit return from the destructive opener who was beaten in flight.
Having scored his runs off just 73 balls, including 12 fours and one six, as India reached 113 in just the 24th over, Sehwag's dismissal naturally led to an immediate reduction of the run rate.
Left-hander Gambhir began to be more proactive once he reached his 13th test half-century but he had been very circumspect for a large portion of his stay after surviving an eventful first over at his level by McKay, the pick of the attack despite going wicketless.
In just the ninth over McKay had a good shout for leg before wicket turned down off his very first delivery when Australian umpire Simon Taufel gave Gambhir the benefit of a doubt to a ball which may have been going over the top.
Gambhir poked unconvincingly at the next ball which he edged along the ground through the slips and was then beaten outside the off stump by the fourth ball.
McCullum was sure to spend more time on the team physiotherapist's table tonight after he experienced back spasms when landing awkwardly during catching practice immediately before the toss yesterday.
That meant he was shuffled down the order to No 8, vacating the opener's role where he starred in the drawn second test at Hyderabad with a career best 225.
He was in obvious discomfort in reaching 34 not out by stumps and did not last long this morning despite moving more freely.
After resuming with New Zealand at 148 for seven this morning, McCullum's innings ended when he flashed once too often outside off stump to present a catch behind the wicket off fast bowler Ishant Sharma, who ended with the fine figures of four for 43 off 18 overs.
Injured McCullum battling on in third Test
Jesse Ryder limped his way to 59 and Brendon McCullum, fresh from a test best 225 in the second match at Hyderabad, battled a back injury to be unbeaten on 34 as the tourists stumbled to 148 for seven by stumps in their first innings.
Following a delayed start caused by a damp outfield, the day began promisingly for New Zealand as skipper Daniel Vettori won the toss, but it turned ugly from there as opening batsman McCullum almost simultaneously went down with back spasms suffered during warmups.
It prevented McCullum joining Tim McIntosh at the top of the order, with first drop Martin Guptill instead promoted one spot while McCullum remained in the dressing room undergoing treatment.
Team management said only that McCullum would bat lower in the order, and his services were called upon sooner rather than later after New Zealand made a shoddy start to slump to 82 for six barely overs after tea when Gareth Hopkins edged left-arm spinner Pragyan Ojha to slip.
McCullum was clearly in discomfort, running gingerly and regularly stretching his back as he collected a series of singles, while at the other end Ryder went to his sixth test half-century in 131 minutes despite a possible recurrence of a calf strain which flared during his hundred in the first test at Ahmedabad.
He and Ryder put on a stand of 42 for the seventh wicket before Ryder was dismissed after three hours when he slammed a back foot drive off spinner Harbhajan Singh to Suresh Raina at cover.
McCullum resumes tomorrow with Tim Southee, who is on seven.
Neither McIntosh nor Guptill stayed around long, both victims of Shantakumaran Sreesanth, who is something of a loose unit but a fast bowler capable of producing quality deliveries.
He came up with two of them to remove the makeshift opening combination in successive overs.
He found a perfect length to induce the thinnest of edges behind from the bat of Guptill on six and McIntosh went next for four when he was beaten for pace by a ball which clipped the top of the off stump.
Ross Taylor, the only specialist batsman not to cash in this series, again missed out after employing his trademark cut to quickly advance to 20.
He was then dragged on to the front foot by recalled fast bowler Ishant Sharma, playing here only because of an injury to left-arm quick Zaheer Khan.
Taylor leaned forward defensively as the ball skidded into his front pad, and Australian umpire Simon Taufel upheld a vociferous appeal despite suggestions that ball struck Taylor outside the line of his off stump.
At 42 for three, Vettori must have had serious misgivings about his decision to bat first.
Those doubts deepened when Kane Williamson came and went in the space of five minutes to make it 43 for four after the 20-year-old scooped up a soft catch to cover off Ojha.
The captain's mood would not have brightened either as he became the next victim for just three.
Vettori had not had time to get his eye in when he attempted to pull a short ball from Ishant outside off only to drag it on to his woodwork.
Earlier, play was delayed for three hours due to a damp outfield at VCA Stadium following a heavy downpour yesterday afternoon.
After taking an early lunch officials announced amended hours of play, with two sessions from 1230 (2000 NZT) to 1440 and from 1500 to 1730.
The wicket block itself was fine but one end of the ground was wet and required a substantial amount of sawdust and light rolling as it remained out of the direct sunlight because of the double decker stand that surrounds the 60,000-seat venue.
Why remedial work was not carried out yesterday following the hour-long downpour is a moot point but workers were outnumbered by supervisors as they went about their duties this morning.
The New Zealanders, too, were in need of supervision.