The tourists had set a competitive total of 257 from their 50 overs, only to see the Indians win through with 15 balls to spare.
However, despite the outcome, Cook feels that his side performed well.
"That partnership between Suresh Raina and Rohir Sharma changed the momentum of the game," he said. "But I think we put on a good performance, the conditions were not quite in our favour but I thought we played quite well.
"It nipped around a bit throughout our whole innings and it skidded on a little with the dew, but we thought we would do well if we could set it up for the last 10 overs."
The defeat has resulted in England losing the five-match series, despite having one game left to play.