Cook's opposite number Mahendra Singh Dhoni found himself in the unaccustomed position of trying to explain an ODI defeat.
He said: “Three hundred was par score today, and we gave away quite a few soft wickets in the middle order.
“We lost too many wickets and were not in position to chase the runs, so those dismissals really cost us the game.”
Dhoni has another chance to finish India's tour with a win, in Sunday's NatWest Twenty20 back at Edgbaston.
Cook, by contrast, signs off with minor encouragement after series defeats in both Tests and ODIs against Sri Lanka, and a win and a loss against India.
“The bottom line is we have lost a series,” he said, before reflecting on a decidedly mixed first season of his and coach Peter Moores' new era.
“I feel tired,” he said.
“When we've played well, we've played really well - and when we've played badly, we've played pretty badly as well.
“It's always interesting (in this job), and this is just another interesting summer.”
