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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Kohli also explained why leggie Amit Mishra is in the squad even though youngster Yuzvendra Chahal was picked ahead of his senior teammate.
"In 2014 World T20, he did really well, it was unfortunate that he was not part of the squad in 2016. He is a guy with variation and is any day useful on a bare wicket," he said.
He was also all praise for the English bowlers and said his team put up a below par total today.
"If we bowled we could have made good fight of the total but I think about 170-175 would have been competitive. It won't say a match winning one still because the ball was coming on nicely. With the start they had, it would was very difficult to pull things back.
"Their fast bowlers bowled well on that wicket. They bowled good lengths. It wasn't east to connect, you had to stand upright and take the risks. They (England bowlers) showed character. They deserved to win, they were better with the ball, more smart. Even in death they hit some really nice areas. Even Tymal Mills was good with the slower bouncers.
"They played well. You could tell that they are playing more freely which was evident in their body language. There were some loose shots from us as well, which led to us being 30-35 runs short."
He also praised opposition captain Eoin Morgan for his match winning knock.
"He has been backing himself since the ODI series. You could see the team is more expressive in the shorter formats. Not thinking of the outcome too much. You have to give credit where it is due. They are pulling off good shots. We have tried to make them play against spin but they have come out on top. I am wary of his ability. He is a world class player.