Warne criticised the England captain for using "boring and negative tactics", adding that his lack of imagination could cost the tourists a series victory in Australia this winter.
While Cook, who led England to a 3-0 success over their greatest rivals this summer, claims 'he will not lose any sleep over the comments', he is aware he could be a bit more adventurous in his approach.
Speaking to Sky Sports News, Cook, who has lost just one Test match in 14 since taking over the captaincy from Andrew Strauss in August 2012, said: "I'm not going to get into the nitty gritty of my captaincy. I'm not sure that's really what this is all about.
"This is what happens when England play Australia. It happened in the summer and I don't expect anything to change over the next couple of months.
"I have always said I am trying to learn my job, trying to learn from experience, and I'm sure there are times when I could be slightly more imaginative and think slightly differently if the situation arises.
"But we have had a pretty good run so far as a Test side.
"In my first year as a Test captain we won away in India, which hadn't been done for a long time, we won a series against Australia and I think they are things which we can be very proud of as a side.
"There is a lot more interest in what is going on in the game today, and how you handle yourself, and over a pretty long period now I think I have handled it pretty well.
"People will understand that when someone makes a comment about you it does change your blood pressure slightly but I'm pretty confident in my ability to handle it as I have done it pretty well over the last seven years."
Former Australia skipper Steve Waugh has laughed off any suggestions that Warne's comments will have a negative effect on Cook's performance.
"I think as a captain you do the job you have to do. England won 3-0 in the summer and you can't argue with that," Waugh told Sky Sports News.
"As long as your own players respect you - and I think the England players respect Alastair Cook - then I'm sure that's all he is concerned about.
"The comments from Shane will be water off a duck's back. Alastair will just go out a do his job and if his side is winning then there's not much else he can do."
Cook has also backed England batsman Joe Root after Warne claimed he would be "crucified by Australia's pace attack if he opened the batting".
"Joe can bat in any situation," said Cook. "He is a fantastic player and I think anyone who saw his 180 at Lord's and his 100 against New Zealand will have seen the class he has.
"He has been outstanding for us in all forms of the game and being able to bat in any situation is one of his greatest strengths."