Rodgers will miss having Carragher around for a variety of reasons and he knows he is impossible to replace.
"I don't think there are many about like that, I've got to be honest," he said. "What he's got at this football club is unique. You have to find different ways. All great players, their time comes to an end.
"We need to find a good one now to come in and support the group - and it certainly won't be easy.
"He's an incredible player and a real gentleman. You saw his performance today - his ambition was to go out at the top and he's going out as a top performer.
"He's played 16 Premier League games since he came back into the team and we've only lost one. He's been an absolutely colossal player and at 35 he's still fit and strong.
"It's with great sadness that he has to move on but we now have to."