But Gooch, who played 118 test matches for England and has been full-time batting coach for the national side since February 2012, said Cook was the man to help rebuild a new-look side.
"I sincerely believe he is (the right person to captain England)," Gooch said in an interview with Sky Sports.
"I don't see any reason why he will not be a successful leader again in the future. Yes, he needs to make improvements. Yes, he needs to look at things himself, the way he goes about things.
"But that's the same with any player, and any cricketer, throughout his career. They're always looking to upgrade and make improvements to themselves and the way they go about their cricket."
England travel to the West Indies for a one-day series at the end of February without Cook, who will take a break following the Ashes defeat, and Gooch is certain the 29-year-old will come back refreshed.
"I'm sure he'll have a good rest," said Gooch, who coached Cook through the ranks at Essex.
"I'm sure he'll look forward to coming back here and playing for Essex at the start of the season."
(Reporting By Michael Hann, editing by Ed Osmond)
