The tourists set the hosts a target of 299, which they eventually reached in a nail-biting final over to claim the series 3-0.
"It's a tough defeat to take, especially when it's so close," said Cook. "Our fielding has been slightly below par, which is unusual for us, and today it cost us 20 to 25 runs in the field. Six an over is always a tough chase, but credit to the way MS (Dhoni) and (Ravindra) Jadeja finished that off."
Cook's side will be able to redeem themselves in the fourth match of the five-game series in Mumbai on Sunday.