CRICKET NEWS - A KL Rahul century was not enough of a platform for the tourists, who made 296 for seven after being put in to bat.
New Zealand, stung by a 5-0 shutout in the recent Twenty20 series, reached the target with 17 balls to spare.
A frustrated Kohli, who admonished his players for poor fielding several times during the match, said it was a fair result.
"We didn't deserve to be on the winning side at all in the series," he said.
"We haven't played so badly, but if you don't grab chances at this level then teams are going to hurt you.
"We didn't show enough composure under pressure. New Zealand did."
It was the first time India have been whitewashed in a bilateral ODI series of three or more matches since 1989 and the only time it has ever happened against New Zealand.
Openers Henry Nicholls and Martin Guptill gave the Black Caps a flying start with 80 and 66 respectively.
Colin de Grandhomme then steadied a mid-innings wobble, bludgeoning 58 off 28 balls to see the hosts finish on 300 for five.
Legspinner Yuzvendra Chahals was the pick of India's bowlers, taking three for 47.
Earlier, Rahul boosted India's hopes with his fourth ODI century, bringing up the landmark off 104 balls, before departing on 112.
He was supported by a gritty 62 from Shreyas Iyer but most of India's batters failed to live up to Kohli's pre-match exhortation to play positively and post a big total.
Prithvi Shaw and Manish Pandey both reached the 40s but no other batters made double figures, with Kohli out for nine.
Still, Rahul looked set to steer India to a huge total before Black Caps paceman Hamish Bennett slowed the scoring with a late flurry of wickets.
Rahul had a life on 64 when Mitchell Santner's throw at the stumps went wide and the batsman made the most of it to score his fourth ODI century, bringing up the landmark off 104 balls, including nine fours and one six.
Bennett dismissed Rahul for 112 and then snared Manish Pandey for 42 off his next ball.
His fourth wicket came when Shardul Thakur sent a full toss straight to de Grandhomme, and the bowler was unlucky not to get another when Navdeep Saini almost edged the next delivery onto his stumps.
The focus now turns to test cricket, with the first of two five-day matches scheduled to begin in Wellington on February 21.
The results of both matches will count toward the inaugural ICC World Test Championship, in which India are runaway leaders at the top of the ladder.
Kohli said he wanted India to display an improved mentality during the tests.
"I'm very, very excited because of the championship every match has that much more importance and we have a really good, balanced team in test cricket," he said.
"We definitely feel we can win the series here but we obviously need to step onto the park with the right kind of mindset."