Carragher hung up the boots last week after his final game in victory over QPR.
"He will be sorely missed by Liverpool and I think it will be a hard task to replace Jamie because he is such a vital cog in the wheel," the 1992 FA Cup-winning captain told LFC TV's new 'Carragher' documentary.
"You can't speak highly enough of Jamie for the things that he achieved and the standards he set at Liverpool. It's going to be a hard task for someone to follow in his footsteps.
"For me he is up there with all the great centre-backs Liverpool have had but not quite as a good as me! [laughs].
"Jamie is easily up there with the best. You are talking about being up there with the likes of Alan Hansen, who was a fantastic player.
"They were different players, so Jamie would be better than Alan at some things and maybe not as good at other sides of the game.
"If you asked an ex-centre-back to describe what a centre-back should be about you would say Jamie Carragher because he was a defender who blocked things, made tackles, put his body on the line and got cuts for the team cause."