Allen made 27 from 20 balls to take the total to 109/8 after debutant Krunal Pandya and chinaman Kuldeep Yadav choked West Indies in the middle, reducing them to 87/8 in 18 overs.
The 23-year-old said it was not the best of wickets and a score of 150 would have made the game competitive.
"It was not the best wicket but we had to be patient, should have played the ball on merit. We were too aggressive; I think we could have easily got 150 or 140, that was the target we were looking for," Allen said at the post-match news conference on Sunday.
The reigning World T20 champions had a four-match unbeaten run coming into the match but they were undone by some fine spin bowling.
"It's one of those days. We will look to come back in the next game. I hope we learn from this and take it to our next game," he said ahead of their second T20I in Lucknow Tuesday.
Despite being named in the squad, hard-hitting Andre Russell pulled out of the series on the eve of the opening game due to an "injury".
None of the batsmen could stay at the crease and execute their plans.
"Anything is possible in T20. it does not matter how many wickets you lose... We could have executed efficiently. It was our first game, we will try to execute our plan and play the ball on merit," he said.
"In T20s, you have to expect anything. It was one of those days. We will just look to bounce back in the next game.
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