"Shikhar and Rohit didn't get a big one. One of the top three has always got the big one. A senior man had to step up and today was my opportunity to step up. It was important to string in a lot of dot balls," he added.
Kohli had a relatively quiet World Cup and this was his first century since March. En route, he surpassed former captain Sourav Ganguly to become India's second highest run-getter in ODIs.
The India skipper also shattered a 26-year-old record when he surpassed Pakistan's Javed Miandad for most runs by any batsman in ODIs against the West Indies.
Kohli said it was a good toss to win as the wicket became difficult in the second innings.
"Good outing with the bat. Exactly why we wanted to bat first. If you saw the later half of the West Indies innings, it was difficult to bat on. I think the rain in between helped them else it would have been tough to bat in the middle," he said.
"The batting became a little easy thanks to the rain when (Shimron) Hetymer and (Nicholas) Pooran were batting together.
"It was tough gripping the ball when it went into the outfield. It was about staying in there and hoping one wicket will put pressure on them and luckily we got the wickets."
Kohli said the number of left-handers in the West Indies team prompted him to play Kuldeep Yadav in place of Yuzvendra Chahal.
"The number of left-handers work in favour of Kuldeep and that's why we went in with him rather than Chahal. He is more lethal against the left-handers because of his variations and the lines that he bowls to them," he said.
"Kedar (Jadhav) was precise as well. With the number of left-handers, you want to go with a chinaman bowler rather than a leggie. With Jadeja playing, it helps our balance."
The skipper lauded Shreyas Iyer, who made a crucial 71 on Sunday.
"He (Iyer) is a very confident guy and has the right attitude. Really got the tempo going and took the pressure off me. After I got out, he got the extra runs as well," Kohli said.
West Indies captain Jason Holder said losing the last six wickets for just 62 runs cost his side the match.
West Indies were comfortably placed at 148 for four after the 27th over before they lost wickets in quick succession to be bundled out for 210 in the 42nd over.
"Extremely disappointing. We bowled really well and the game was in our hands. We lost crucial wickets at the back end to lose the game.
"We need to take responsibility. We need to take the game deep. The pitch was pretty good and the bowlers despite the humid conditions did well. The batters have to take the responsibility. They have been letting us down far too often," Holder said.
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