England are on course for a 5-0 whitewash - for only the third time in their history, but second in three tours for Cook - after losing the fourth Test by eight wickets at the MCG.
Cook and coach Andy Flower must therefore somehow try to work out how to fight back in Sydney next week, before it is too late.
Chris Rogers (116) and Shane Watson (83 not out) made a mockery of England's hopes of making Australia sweat a little at least, in pursuit of 231 to win on day four here.
A 4-0 scoreline is therefore the current culmination of a dramatic collective under-performance on a tour which began with hopes of a fourth successive Ashes series victory.
This time, England threw the match away with a second-innings collapse - a variation on a theme which left Cook again having to face some blunt questions.
One included a hint that his leadership might be a significant part of the problem.
"Yes. It's something you do look at as captain and leader of the group," he said.
"(But) I feel as if we are doing the right things. If I didn't think we were doing the right things, we'd have changed the way we are approaching things - training and all that.
"I think we're preparing in the right way, but just not delivering it out there - or Australia aren't allowing us to."
Cook insists he is still enjoying his role, despite a miserable campaign in which England have managed to stay competitive so far for only two days out of 18.
The 29-year-old acknowledges too, though, that when it comes to England's performance and fortunes the buck will stop with him.
"In a strange way, I'm enjoying the job and I'm enjoying the challenge," he said.
"I'm totally responsible as captain for the team - and if, at the end of the series, the selectors decide I'm not the best man for the job then so be it.
"It would hurt, and I've got no plans of going anywhere."
He has one more Test to try to stave off that sort of judgment.
"I'm desperately trying to use as much of my experience of playing 100 Tests to help turn this team around," he said.
"I know that it starts with a lot of hard work and it starts with a performance or two that we jump on the back of.
"But if someone says there's a better man for the job, then I have to take that on the chin."
It was all the harder to take for Cook in this match that England put themselves in position to push for victory, yet then lost within three sessions.
"The part of this game that makes it even more frustrating is that we got ourselves into a good place to put some pressure on Australia - 100 ahead and no wickets down in the second innings," he said.
"I suppose that might be where we are as a side.
"When you're winning games of cricket, you get yourself in a good situation like that and you really take advantage of it.
"But when the confidence isn't there and you lose a couple of wickets, you probably (don't).
"You can give Australia some credit. They jumped on us when they had an opportunity.
"They got me out. We're 65 for one, and then for that next half an hour of cricket they dominated us - and we couldn't respond to it."
England still thought they had a chance at the start of day four, which Australia began on 30 without loss - but dropped catches, including one by Cook, were something they could not afford.
"We know 240 is always an interesting run chase when you get three wickets early," he said.
"We created three chances in that first half an hour... something we knew we'd have to do, and we didn't take them.
"That's the simple deal.
"I can only explain my one, where I saw it all the way and was in a good position. Maybe I wanted it too much, and I snatched at it."
Australia captain Michael Clarke had no such regrets, of course, and was especially pleased with the resilience shown by his team - who have previously dominated throughout, apart from day one of the first Test.
He said: "I think it's a very special win for a number of reasons... (starting with) the fact that a lot of people thought we would come here complacent and not have the same willpower to continue to play the same way as in the first three Tests.
"Also for the first time in this series, we found ourselves behind in the game - and over the last couple of days, we've been able to turn that around and win convincingly.
"I think the boys deserve a lot of credit."
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