After being put into bat, India made 129/7 off 20 overs after rain delayed the start of the match. In reply, the hosts could only manage 124/8.
"With 20-odd needed off 16 balls it was in our hands. There have been a lot of good performances, but at the moment we are a bit devastated," said Cook at the presentation ceremony.
"We've come up a little short. I thought we bowled well, you'd take 130. It's tough to take at the moment. I think both sides found the pitch quite hard to bat on. You are always going to think of different reasons. I'm proud of the way the players have performed in this tournament," added the left handed batsman.
England had previously reached the final of the 2004 Champions Trophy when they lost to the West Indies.