Warne, one of cricket's greatest bowlers and who is close to current Australian coach Darren Lehmann, has been a constant critic of Cook since the 29-year-old replaced Andrew Strauss as test captain, accusing him of being "negative" and "boring".
Cook defended himself during the drawn test with Sri Lanka at Lord's which finished on Monday, with some suggesting an earlier declaration on the fourth day may have given England a better chance of bowling the tourists out in their second innings.
He did likewise in a BBC radio interview with Jonathan Agnew on Thursday.
"Something needs to be done, because for the three years of being England captain I have in my eyes been criticised for a hell of a lot of that," Cook said ahead of the second and final test starting Friday at Headingley.
"Yes when you lose games of cricket you get criticised. But I've also won a lot of games of cricket for England, won more one-day games as an England captain, I won an Ashes, I won in India away, and that's what I'm proud of as well,” he said.
"So to be criticised for three years totally with those results I find quite hard to take to be honest with you," he added.
He was asked whether he thought Warne's criticism was personal. "Yeah I think it is, yeah," Cook said.
Under Cook's leadership England have won nine and lost six of the 22 tests where he has been in charge, including the recent 5-0 Ashes defeat in Australia.


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