Only a near unmissable catch by the captain himself, to end Ajinkya Rahane's fun on a mere 106, stopped England losing by 10 wickets at Edgbaston.
The hosts mustered only 206 all out, despite Moeen Ali's 67, and were then powerless with the ball as Rahane and Shikhar Dhawan (97no) put on 183 for India's first wicket in a chase that lasted only 30.3 overs.
It is hard to imagine a more one-sided contest and, after India had gone 3-0 up to inflict England's fifth series defeat in their last six, pointed questions about Cook's future as one-day international captain were all too predictable.
As in this summer's Test series against India, which he eventually helped to turn round 3-1 in England's favour, Cook did not shirk the inquiries - and made it clear he intends to stick around for the World Cup in Australia and New Zealand early next year.
Asked that very question, he said: "If I'm allowed to be, yes.
"I don't have a say on selection, but I've captained for three-and-a-half years with the goal to try to win the World Cup in Australia.
"I know that seems a bit far-fetched at the moment when we're losing games of cricket, but there're a lot of really good players in that changing room.
"If we can improve at the rate we need to improve, we've got a chance and that's what we have to believe in.
"I know when you lose games of cricket, no one (else) does, but in the dressing room we have to."
For the third successive match, England were not just beaten but trounced.
"It was a tough performance to take, to lose by nine wickets," Cook added.
"We were behind the game very quickly and we never got back into it.
"They're playing better than us at the moment and they're the number-one ranked side in the world for a reason.
"They're the benchmark and 50-over champions as well. So we're testing ourselves against a very good side and at the moment, coming up very short."
England's next assignment is to try to avoid a series whitewash at Headingley on Friday.
"It's a really tough place at the moment, but it's amazing how quickly you can turn around," said their captain.
"We've got to stay true to our beliefs as a team and actually the belief you have as a player, because when you lose games of cricket people chip away at you and you start doubting the reason why you probably got selected in the first place.
"Maybe for a few of these guys, it's the first time it's happened that we've lost as badly as this and it's a true test of character for the whole team, really."
Cook's critics point to his own sub-80 strike rate at the top of the order.
He does not believe it is any lack of attacking intent that is the root of the problem, just that he and his fellow batsmen keep making mistakes.
"I don't think it's been our mind-set really," he said.
"I think it's been our lack of execution of fairly basic skills at the moment with our batting.
"As a one-day batter, you need to be able to score at a good rate, at certain times take low-risk shots for a while, but have the option of putting the pressure back on the (opposition) but also staying in.
"Unfortunately, we're not doing that."
Neither does Cook give any credence to the suggestion that Test cricket matters more to Englishmen than the 50-over format, in which they have never yet won a world tournament.
"You only have to look at the dressing-room to see whether it matters or not now," he said.
"We're brought up in a country where Test cricket has huge importance.
"But just because you put huge importance on Test cricket doesn't mean one-day cricket doesn't count.
"We've got a World Cup in six months. That's our big focus now.
"There is no Test cricket for six months, so it is very important."
He acknowledges his fate may yet be decided by others, such as England and Wales Cricket Board managing director Paul Downton, but insists he will not be leaving his post of his own volition.
"They're the guys at the top of English cricket and if that's their decision then I have to take that on the chin," he said.
"I hope it's not, but if it is, it is.
"I believe at the top of the order that, if I bat for 40 odd overs, I will score enough runs at a good rate.
"That's what I have done when I've been batting well."
After 38 ODI innings without a century, it is some time since he could claim he was.
For India, there are no such problems.
Cook's opposite number Mahendra Singh Dhoni said: "We have kept improving from the first ODI on ... (this was) a complete game for us."
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