Rodgers now hopes he can persuade Carragher to carry on next season.
"I had a good conversation with Carra last summer because he was maybe thinking about moving on to pastures new last year, but we talked and decided that he would stay.
"For me, he's hardly put a foot wrong. I obviously wanted to go with a pairing of Martin Skrtel and Daniel Agger as maybe the future at the beginning of the season and those guys have done really well.
"But I felt that with Carra and all the games he's played - the cup games and any time he's come in in the league - he's been remarkable and I felt I wanted to put him in the team."