Carragher bowed out in his 737th match for the Reds in yesterday's 1-0 win over QPR after Philippe Coutinho scored the only goal in the 23rd minute.
But the result was almost a sideshow as Carragher took centre-stage for one last time.
Rodgers needs to strengthen his defence in the summer but accepts it is pointless trying to find someone who can do the job Carragher did.
"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've seen it here through the years. You look at Ian Rush when he went away and they brought in John Barnes and Peter Beardsley - and they brought something else.
"We need to find a good one now to come in and support the group - and it certainly won't be easy."