Laxman returned to form with a century in India's first- innings total of 362 before West Indies reached 113 for four in their second innings to take a big lead of 332 into the final day.
"It's good to get a hundred, especially when the situation demanded it, it was important that I got a big score," Laxman told reporters.
"The team management has always given me the kind of responsibility demanded of a senior player, and I'm happy that I've been able to contribute as a senior player should."
Laxman's performance was his 10th Test century and his first major contribution of the series.
A string of low scores put him under pressure to retain his place after he was dropped for two Tests in the recent series against England.
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"Good teams always have such competition, but when you're playing a match you don't think of selection.
"You just go out and play to the situation and try and give your best.
"You have to concentrate on the things which you can control and leave the rest to the selectors and the team management."
Laxman batted at number three in St Kitts, an unfamiliar position for him in Test cricket.
"When you're playing international cricket you have to get used to batting in any situation and in any position," Laxman said.
"I've always enjoyed batting at number three, although I've not batted there as much as I have at number five or number six for India."