"Whatever you do when you win or lose the toss you want to do well. We weren't quite good enough at the top but credit to the way India bowled," he said.
"Their opening spell was very good, it put us under a lot of pressure and hit the mark with their lengths on that surface."
New Zealand's 230 for nine was inadequate but Kohli liked what he got out of his team today.
"We thought the wicket was going to play a little slower during the day so it would be better to bat on in the evening and that's exactly how it turned out," India's batting champion said.
"We still needed a good performance with the ball and I thought the bowlers were really clinical today and the fielders so I'm pretty satisfied with the win."
Allrounder Colin de Grandhomme impressed with his positive strokemaking on his way to his best ODI score, 41 off 40 balls, and drew praise from his captain.
"It wasn't easy to play fluently but he came out and played really nicely. He scored at better than a run a ball and we saw in both innings that wasn't easy to do.
"It was a nice contribution but it would have been nice to have a few more runs on the board," Williamson said.
Still, New Zealand will draw confidence from their win in the first game of the series as they prepare for a big chance to win a maiden bilateral ODI series in India.