Ashwin took 10 wickets and also scored a 40-run cameo in the Indian first innings, playing a crucial role in the 197-run win in the match.
"He's been outstanding for the Indian team. If you see all the impact players in the world, he comes in the top three-four easily. There are quite a few players making big impact for their respective sides. Especially bowlers. Bowlers are the one I feel that win you Test matches and Ashwin is one of them," Kohli said after India's big win.
"Very smart cricketer, very intelligent. That shows in his batting as well. He understands the situation and plays accordingly. He knows when to get runs and when to play the situation out accordingly. So it's priceless to have a cricketer like Ashwin in your Test team," he elaborated further on the skills of his premier spinner.
The captain also spoke on how both Ashwin and Ravindra Jadeja, who shared 16 of the 20 Kiwi wickets in the match, take lead when things do not pan out as planned.
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"As a captain it always gives you more assurance that both these guys obviously know what they are doing and they are going to pitch the ball in the right areas. Both of them are pretty open to hearing suggestions, but when they feel like they are very convinced about what they want to do, they tell you that. And I personally like that as a captain as well," he said.
"He is someone who absorbs the pressure really well but after a certain stage in the innings there comes a time when the team needs runs. That's where we felt that he has the ability to capitalise. It was just about conveying that to him. He has worked hard on his game.
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"If you see his double hundreds against England and Australia, he will dominate spinners. That's exactly what we wanted him (Pujara) to do. We didn't want him to go into a shell. We want Pujara to bat to his potential. Once he starts scoring runs to go with the composure he already has, it becomes very difficult for the opposition to have control of the game," Kohli added.
"It wasn't much of a concern because the reason we scored the extra 30-40 runs was because we could bat them out of the game. That's exactly what we planned to do. A target of 430 on the fifth day wicket - fourth day one session and a fifth day wicket - is very very hard to get. All your batsmen right till No 10 have to bat really, really well. So we knew that it was a matter of being patient. It's a good lesson for us, good learning," he said.
Kohli said there will surely be a psychological advantage over New Zealand now but they can't afford to be complacent since they are up against a team that fights hard.
"For them to show the resilience and the character that they did over the five days of this game, we know that we cannot afford to be relaxed at any stage. We got relaxed in phases in this game and they capitalised you know, they were on the mark throughout the game.