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.
"So to be criticised for three years totally with those results I find quite hard to take to be honest with you."
He was asked whether he thought Warne's criticism was personal.
"Yeah I think it is, yeah."
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.
(Reporting by Josh Reich, editing by Tony Goodson)
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