England slumped to a 95-run loss in the second test at Lord's on Monday, the middle and lower order blown away by a short-pitched barrage from seamer Ishant Sharma, who took career-best figures of seven for 74.
The loss took England's winless streak to 10 tests, having lost their last two series to Australia and Sri Lanka, and means they must win two of the three remaining matches to have any hope of beating India.
Serious questions are now being asked about Cook's suitability for the captaincy, and having scored 115 runs in his last seven innings, he is struggling to justify his place at the top of the order as well.
"If I'm not scoring runs by the end of the series and losing more games, it becomes tougher and tougher doesn't it," Cook told reporters.
"I'm clearly maybe not the man to turn it around.
"I've been speaking Mooresy (coach Peter Moores) over the past couple of days, even in tough times, and me and him still think we can turn it around."
The 29-year-old admitted he did have doubts, but was determined to remain captain until it is taken out of his hands.
"It's hard when you lose, there is no mistake about that, it's a tough job when you lose games of cricket and it's even tougher when you're not scoring runs," he said.
"I'm not going to hide and say I'm waking up every morning the best I've felt in my cricketing career at this precise moment in time.
"But, if and when we turn this around and when get 11 people working close to their potential and we get win a game of cricket and it changes, that moment of going through tough times will make it feel a lot better."
Former England skipper Michael Vaughan said Cook should be replaced by Eoin Morgan, who has not played a test since 2012.
"A real decision needs to be made about Alastair Cook," Vaughan told the BBC.
"I look at the way he's played - he's not scored a hundred in 27 innings, tactically he's been all at sea for a while now.
"Go and spend four or five months away from cricket. He's 29 years of age, he's been in this environment for eight years non-stop. That takes its toll as a player never mind with the captaincy burden as well."
While Cook has been battling, he has not been helped by the form of a number of his senior players.
Fellow batsman Ian Bell has made starts but failed to push on, Stuart Broad has been down on pace, and wicketkeeper Matt Prior is struggling with the gloves and bat.
The new generation of players such as Gary Ballance and Moeen Ali has shown plenty of promise, but cannot be expected to carry their more senior team mates.
"Myself, Ian Bell, Stuart Broad and Matt, we haven't played as well as we can," Cook added.
"Test cricket is really tough environment to survive in and play, the game unfortunately owes you nothing just because you've done it in the past, you have to keep performing for England."
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- Alastair Cook