But he told a news conference on Tuesday that he does not feel out of form, despite coming under pressure not just for his paucity of runs but also a perceived lack of attacking instinct as captain.
Having spent 10 days away since losing the second and final test to Sri Lanka, the left-hander said he was ready to start contributing with the bat.
"I never have felt that I've been hitting the ball particularly badly this summer - I scored some runs for Essex at the beginning of the season and I haven't managed to transform that into runs for England," he said.
"I know how important it is at the top of the order to do that and I'm desperately keen to lead from the front and score some runs.
"As a batter especially, you're in there because you are one of the top six batters in the country and your job is to score the runs to set up the game for England. Doesn't matter if you're captain or not.
"I haven't been doing that over the last year or so, and no-one's keener than me to put that right," he added. "I know I've got to score runs at the top of the order in this series."
Cook did not think leading the team had interfered with his job of laying a strong platform for England's middle order, having seen his side fail to register a win in their past eight tests and slump to series losses to Australia and Sri Lanka.
HUGE HONOUR
"It's a huge honour to do this and I can go to sleep knowing I've thrown everything I've got into it," he said.
Cook was confident Matt Prior would be fit to keep wicket, despite hurting his thigh in training on Monday, and said the selectors faced a tough choice regarding Durham all-rounder Ben Stokes, back in the squad, having taking 10 wickets for his county.
The place of newcomer Chris Jordan, who performed well in his first two tests against Sri Lanka, appears most at risk should Stokes be selected.
India have only three players in their 18-strong squad - captain Mahendra Singh Dhoni, seamer Ishant Sharma and opener Gautam Gambhir - who have played a test in England previously.
Rahul Dravid has been asked to mentor the younger players as they look to win their first test overseas since 2011.
"We wanted a mentor with the side who can talk about his past experience, a lot of stuff but not just talking about technical things," wicketkeeper-batsman Dhoni told reporters.
"A lot of it is [Dravid] interacting with the youngsters, and they are comfortable talking to him.
"We noticed that in South Africa. He was part of the commentary team and they'd go up to him and approach him, have a chat whether it's cricket or something else."
(Reporting by Josh Reich, editing by Neville Dalton)
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