Cook found himself under the spotlight after England's recent 5-0 thrashing in Australia, a campaign where the opening batsman managed just 277 runs at an average of under 28 per innings.
Team director Andy Flower resigned and one-day coach Ashley Giles was axed following England's embarrassing defeat by the Netherlands at the subsequent World Twenty20 in Bangladesh.
"Disconnected" star batsman Kevin Pietersen was sent into international exile but the England and Wales Cricket Board hierarchy remained strong in their support of Cook.
"I think it would be wrong if I didn't," he added.
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"We'd lost a lot of games and we hadn't played to the standard that side was capable of, and the stuff we were doing was not making a difference. If you don't question your position as leader then, you never will."
But with backing from the likes of Stuart Broad and Ravi Bopara, a longstanding colleague of Cook at Essex as well as with England, the left-hander decided to carry on as skipper.
"I spoke to Stuart Broad and Ravi Bopara and they said 'no, you must carry on'.
"The ECB (England and Wales Cricket Board), since Paul Downton's come in, they've backed me and we've got to justify that confidence.
"It's a great honour to captain England, when we walk out at the venues and they announce the England (team) led by me it's a great feeling. But you've got to be winning games of cricket.