India's 95-run victory piles even more pressure on Cook as he searches to improve both his own and his team's performances before another series slips out of his fingers.
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Ishant Sharma was the latest opposition player to cause havoc to England's batsmen as he took 7-74 to bowl England out for 223, but Cook remains defiant that he will not leave his role.
"It gets harder and harder the more we don't win and of course that heaps [pressure] on you at the end of the day," he said in his post-match interview.
"Until that bloke taps me on the shoulder and says 'we don't want you to captain' I'm desperate to try to turn this around for England.
"If I'm not good enough at the end of the summer then so be it, but I'm trying my heart out to do this and I need to score runs and need to start winning, but I'm here to as long as I'm wanted."
The 29-year-old also admitted that his senior players need to raise their game if England are to get back into the five-match series, which India now lead 1-0.
"The older guys are not playing well as their records suggest," he added. "You need nine or 10 of them playing really well and that is not happening at the moment.
"There is definitely an issue with confidence and getting over the line, we have not won for a long time and it will take some serious performances to drag us over the line."