India need to dominate Test matches and players cannot be content with just looking to improve, captain Virat Kohli said after the tourists thrashed West Indies by an innings and 92 runs in the first Test in Antigua on Saturday.

The margin of the victory, secured within four days, was India's largest outside Asia and gave the side a 1-0 lead in the four-match series.

"We are not at a stage now where we need to come and improve," Kohli, who scored his first double hundred during the Test, told reporters.

"We should be ready enough in international cricket to start dominating Test matches and win those crucial situations and sessions. That's how we become a better team.

"If you think we are going to keep learning every series, learning every game, we will never get that hunger and that mindset to win games from difficult situations.

"We need to challenge ourselves a little bit, which this team has been willing to do and which is a wonderful sign. The way we finished the Test, it all panned out pretty nicely."

While Kohli has led India to a Test series win in Sri Lanka and beat South Africa 3-0 at home, their record outside South Asia in the longest format has been poor.

They have lost series in South Africa, New Zealand, England and Australia on tours since late 2013, something new coach Anil Kumble has said he wants to rectify.

The 27-year-old Kohli replaced Mahendra Singh Dhoni as India's Test captain after the wicketkeeper-batsman retired from that form of cricket during the tour of Australia in late 2014.

Kohli wants his side, who are currently second behind Australia on the International Cricket Council Test rankings, to target consistency as well as wins.

"If we have a chance to win 4-0, then why not," Kohli said. "We don't need to get complacent. If we end up getting a 2-0 lead, it's not that we would be playing for a draw in the next two Tests.

"As we know, if we learn to win Test matches, then we'll learn how to win Tests everywhere.

"We will learn how to play in different situations and we will know exactly what to do when a certain situation is going a certain way."

Kohli hailed his bowlers' attitude, who dominated the West Indian batsmen in both the innings. If the pace duo of Mohammed Shami and Umesh Yadav snared eight scalps among themselves in the first innings, it was an one-man show from Ashwin in the second essay.

"It was a very good effort from the bowlers. The good thing was that we did not bowl that much in the first innings, so everyone's mindset in the second innings was, yes, we can bowl again. I think the first innings ended at a perfect time for us last evening, and then we got 13-14 overs and got a wicket again," he said.

"So it was good to get some rest in the evening, and the bowlers' attitude was very good, all of them voluntarily said, yes, we will bowl, and the spinners took the responsibility."

"They knew the fast bowlers had done a lot of bowling in the first innings, so we will have to take that responsibility. Ashwin obviously bowled very well, and Mishra also bowled very well but didn't get (many) wickets.

"But both kept the pressure on, and we talk about partnership bowling - that was a classic example, that the spinners didn't have to bowl that much in the first innings, but took the responsibility from the fast bowlers in the second innings, and did the job fully.

"All in all, as a bowling unit, it was good execution, and the bowlers will be quite pleased with their performance, and as a captain I am pleased too," he added.

Calling it a great start for new coach Anil Kumble's tenure with the team, Kohli said Kumble was happy with the way the team executed the plans during the match.

"Having played for so long I think he (Kumble) understands how the players feel about a victory. He congratulated everyone and gave special mention to the guys who made important contributions in the game.

"It might not be seen too much but those important breakthroughs and moments are very crucial for the team to win. He understands that very nicely and he was obviously very happy with the victory. It's a great start for him - first game as coach and we end up winning by an innings. We are very happy all round," said Kohli.