Carragher has taken criticism from Reds fans after conceding a penalty for the defeat at Stoke City.
But Redknapp says: "I'm sure Carragher will one day end up as manager of Liverpool, he's one of the great characters in football. Last year, when we played them Carragher did his shoulder.
"He was in agony, but as he was coming off he was telling the doctor to slow down. And he was shouting at the geezer who was coming on to replace him, 'Hurry up, get your f****** gear on.' He wasn't going to leave the pitch until the other boy was ready - no matter how much he was hurting. Different, very different; but that's Carragher, isn't it?"