England drew the series 0-0 after batting out the fifth day of the final Test match, but Cook believes that his side could have come home with the spoils had he been more "pro-active".
The 28-year-old told Sky Sports News: "I could have been more pro-active at times in New Zealand.
"I can't change who I am as a captain. If you ask me to become more like Michael Clarke, Brendon McCullum or Ricky Ponting, I can't be like that. I have to be Alastair Cook.
"But, you can take things from different captains and their styles, and looking back, maybe I could have been a bit more adventurous at certain times."
Cook will skipper England when New Zealand arrive in England for another three-match series later this month, with the first Test commencing on May 16.