According to Rush, Bootle-born Carragher's importance to the Liverpool side can only be truly felt now that he is unfortunately sidelined for up to six months with a broken leg.
Rush said: "If there is one phrase I've heard more than any since Sunday it's probably 'we didn't half miss Carra. I think those supporters who didn't give Jamie enough credit when he was in the team have come to realise just what a great defender he is.
"It's a bit unfortunate for Jamie it may have taken a serious injury for him to be appreciated as much as he should be. When he's back, I'm sure he won't have the same problem again."