It took England only 33 minutes to go very quietly on the final morning – apart from an unseemly exchange in the dying moments between their No 11 James Anderson and match-winning off-spinner Ravi Ashwin – to an innings and 36-run defeat at the Wankhede Stadium which confirmed series success for the hosts, 3-0 with a Test to spare.
England lost their last six wickets for just 15 runs, collapsing to 195 all out to become only the third team in Test history ever to lose by an innings after making 400 first time round.
Cook reflected on “missed opportunities” – to stop Virat Kohli posting a career-best 235 and number nine Jayant Yadav a maiden century in a record stand with his captain – although England collectively had no answer either to the brilliant Ashwin, whose six for 55 gave him match figures of 12 for 127 and took his series aggregate to 27 wickets.
It adds up to five defeats in England’s last seven Tests, with the prospect of a record-equalling eighth of the year in Chennai still to come.
Cook faced a barrage of post-match inquiries as to whether he intends to carry on as captain, and admitted even he does occasionally have doubts.
“Of course you have questions. Naturally you look at stuff,” he said.
England are merely following a succession of other tourists beaten in India, since they were the last ones successful - under Cook, at the start of his tenure, in 2012.
He will be 32 on Christmas Day, and around then expects to be keeping his pre-series promise to review the campaign – including his leadership duties – with England and Wales Cricket Board director Andrew Strauss.
“I will sit down with Straussy at the end of the year – like we have made the pact to do – to talk honestly and openly,” he said. “My position has not changed [whether] we won this game or lost this game.”
Advocates for change have one obvious alternative, in 25-year-old vice-captain Root – and Cook believes his deputy will be able to step up, as and when required.
“I think Joe Root is ready to captain England,” Cook said. “Nothing can prepare you for it. [But] he is ready because he is a clued-up guy who has the respect of everyone in the changing room.”
Cook retains his appetite for the job, adding: “Being captain of England is a huge honour, a huge privilege. It comes onto your shoulders when you win or lose. You go to bed at night and you have to live with making good or bad decisions. I am very proud to do it.”
It did not go to plan in the fourth Test, however.
“It was a game of missed opportunities again,” Cook said. “We missed three good chances to take wickets, and they made us pay. Missing Kohli, missing [Murali] Vijay and Jayant cost us dearly.”
England began the series by dominating the drawn opener in Rajkot, but have fallen short since.
“It is just frustrating,” the captain added. “To beat India in these conditions you have to play the perfect game, and we haven’t managed to do that. If you have to take 14 wickets against these batters in these conditions, it puts you behind a bit.”
England’s spinners Moeen Ali and Adil Rashid have been unable to match Ashwin and Ravindra Jadeja – or indeed Monty Panesar and Graeme Swann, who helped to bowl Cook’s 2012 team to victory.
“No disrespect to Mo and Rash, but Graeme Swann and Monty Panesar were world-class bowlers in 2012,” Cook said. “Mo and Rash have bowled well, but they are not yet in that league of Graeme Swann and Monty Panesar.”
The odds therefore have been stacked in favour of Cook’s opposite number Kohli, who nonetheless insisted success against England has been hard-earned. He said: “I don’t think it’s been easy. We have been put under pressure many times. I would give my team a lot of credit for bouncing back from those tough situations.
“We haven’t been given anything on a platter. We have had to work hard for it.”
India were in danger of falling behind on first innings here, until Kohli and Jayant joined forces.
“We know England are a quality Test side, and we knew they’d try to bounce back,” he added.
“Even in this game, after being 2-0 down, they made 400 runs in the first innings. This is not a team that will throw in the towel.
“If you are a champion team, you have to play like a champion team to win series - and that’s what we did.”