Cook's side dramatically collapsed in the final session of day five to get bowled out for 207 and lose the fifth Test.
Cook's side dramatically collapsed in the final session of day five to get bowled out for 207 and lose the fifth Test by an innings and 75 runs.
The 31-year-old Cook suffered his fourth straight loss as captain after the visitors started the series with a strong performance in the drawn Test in Rajkot.
Questions about Cook's leadership had started doing the rounds after England lost the third match in Mohali and the chorus grew louder as India pocketed the series in the fourth match .
Cook himself admitted that his deputy Joe Root was "ready" for the job, fuelling speculation that he might step down soon.
"I've got to go away and do some thinking. This is not the right time to make decisions as big as that," Cook told reporters at Chennai's MA Chidambaram Stadium.
Cook and company have had a long tour since the Bangladesh Test series in October. The tourists lost to Bangladesh in a Test for the first time as that two-match rubber ended on 1-1.
Cook had earlier spoken of the difficulty of staying away from his family after he flew back home for just 18 hours to be with his new-born daughter in the middle of the Bangladesh series.
"I've got to go away and decide whether I am the right man to take England forward," said Cook.
"When there's not a Test match for seven months it'd seem very foolish to stand here now and make a decision which either you regret or don't," said Cook, whose side is next slated to play a Test series in July next year.
Cook was involved in a 103-run opening stand with Keaton Jennings on Tuesday before India's Ravindra Jadeja wreaked havoc with a career-best 7-48 as the visitors lost their final six wickets for just 15 runs.
"I never feel let down by the lads. I know what everyone's trying to do... I know what it means to them to play for England," he said.
"When you lose games of cricket it becomes very hard and it can be quite a lonely place. You've got to give credit to India," he added.
Cook singled out the opposition bowlers, admitting that his spinners, Moeen Ali and Adil Rashid, did not match up to their Indian counterparts.
"These conditions have tested us to our limits and I really don't want to be disrespectful to Mo and Adil but they are not as good as Ashwin and Jadeja yet," said Cook.