New Zealand team poses with their trophy after wining the series against India 2-0 at Hagley Oval in Christchurch on Monday. AP
Home skipper Kane Williamson celebrated "an outstanding performance" as New Zealand, who won the first Test by 10 wickets, claimed the second by seven wickets to wrap it up 2-0.
But it left Kohli, who was caught making a foul-mouthed outburst to the crowd during day two, disappointed with his top-ranked side.
"We were completely outplayed in this series, and obviously did not play the kind of cricket that we do play as a team," Kohli said. "We were not positive enough, we were not brave enough."
The irritation was clear from the current holder of the "spirit of cricket" award as he lost his world number one batting ranking following a string of low scores.
Kohli gave Williamson a very animated send-off in the first innings and he was caught on camera yelling an obscenity at a group of New Zealand supporters on Sunday.
But he refused to answer questions about his behaviour after the Test.
"What do you think?" he fired back at a journalist, when asked if it was appropriate conduct.
"If you want to create controversy this is not the right place to be. I spoke with the match referee and he had no issues with what happened."
In the two Tests, on traditional New Zealand green wickets, India managed scores of 165, 191, 242 and 124, reflecting Kohli's low contributions of 2, 19, 3 and 14.
New Zealand are now unbeaten in their last 13 home Tests, winning nine of them, and in the past decade their record as hosts is played 39, won 20, drawn 13 and lost five.
India started the day at 90 for six and were all out for 124, before New Zealand chased down the required 132 to win for the loss of three wickets in 36 overs.
The end came quickly for the India innings as Tim Southee and Trent Boult tormented the batsmen with their variety of inswing and outswing deliveries targeting both sides of the stumps.
Hanuma Vihari was the first to fall, in Southee's second over, when he turned a legside delivery too fine and was caught by BJ Watling diving to his left.
Five balls later and with no addition to the score, India's other overnight batsman Rishabh Pant was caught behind off a Boult delivery that swung away.
Mohammed Shami was caught for five by Tom Blundell at deep mid-wicket and Jasprit Bumrah was run out when trying to give the strike to Ravindra Jadeja, who was unbeaten on 16.
Boult and Southee signed for most of the dismissals with Boult taking four for 28 and Southee three for 36. The swing pair accounted for 25 of the 40 Indian wickets in the series.
There was enough seam and swing available for India to keep the New Zealand batsmen guessing but Bumrah and Umesh Yadav were unable to apply consistent pressure and Mohammed Shami was troubled by a sore shoulder.
New Zealand coasted through a century opening stand by Tom Latham and Blundell before losing three quick wickets.
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