The current holders were chasing 179 for five in the second Group E game at the Super Eight stage in Pallekele after Johnson Charles (84) and Chris Gayle (58) clubbed half-centuries.
But the loss of Craig Kieswetter and Luke Wright for nought from three balls put England on the back foot. Eoin Morgan (71 not out) and Alex Hales (68) did their best to rescue an unlikely victory, but Broad’s men must now win their remaining games against Sri Lanka and New Zealand to progress.
Broad said: “We had to regroup. Obviously losing two wickets in that first over hurt us a lot. The way Eoin Morgan played got us back into the game.
“We’re really disappointed, I think it’s a missed opportunity not to win tonight but there are also some positives to take as well. Eoin’s got amazing skill to find the boundaries when guys are still back and he’s been fantastic for us in this format of the game.
“The surface played pretty well. It was quite hard to stop the boundaries flowing in that middle period, but I thought Samit Patel in particular came back pretty well.
“With the bowling effort, I think we were just below par so we’re disappointed not to have chased that.
“It’s pretty clear what we have to do. We’ve done some good things tonight but we’ve just fallen short and we’ve got to stop losing early wickets like that because it’s hurting us.”
West Indies captain Darren Sammy added: “I think it was a very good performance and we backed ourselves to set a target.
“The way Charles and Gayle played at the top really set it up for us. We knew how good the wicket was and it took good work from the bowlers to defend it.
“Looking at all the games played here, we were definitely looking for 200. Once the batsmen get going the margin for error is quite slim and Ravi [Rampaul] setting us up from the top of the innings with two wickets really set us away.
“We saw how England played against India so we decided to maximise our spinners.”
Sammy reserved special praise for 23-year-old St Lucian Charles who, without a century in any form of professional cricket, stayed the course to record his maiden Twenty20 international half-century.
“It was good to see the way he played,” Sammy added. “He started off slowly but he constructed a very good innings, getting his first 50 in Twenty20. Hopefully he can continue doing that.”