Carragher, 35, seemed almost hurt by the fact as he reflected on his career as a one- club man.
He said: "I never really had the option to leave - I don't know whether it was a good thing or bad thing. Maybe no-one rates me!
"I've never even been close. My agent has never rang me up and said, 'This team fancy buying you'. Not once.
"Maybe I was always seen as 'Mr Liverpool', I suppose. You'll have to ask different managers. But I'd never have left in any circumstances.
"Maybe those managers realised that. Or, like I said, they just didn't fancy me.
"And I can't say I ever thought about leaving when I wasn't in the side. You have good times and bad times at your club.
"It's like being a supporter. You don't stop supporting your team because of a bad run.
"And we've had some great times here, won some big trophies. So I feel lucky and privileged."