"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.
"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."
As one career came to an end another was just beginning as 17-year-old Jordon Ibe made his first-team debut and did not disappoint, even providing the assist for the goal.
"I thought he did very well," added Rodgers.
"It's not easy playing at Anfield, his first game here for the first team. As the game went on he became better and better.
"He's got real potential and you can see he's a footballer. He linked up very well with young Coutinho and made some good passes and got some shots off.
"For all the young players, hopefully they'll see from this season that there's hope for them here - that they'll get an opportunity."
Relegated QPR were barely a threat all afternoon and manager Harry Redknapp now faces the task of getting them back into the Premier League.
It seems unlikely it will be with the majority of this squad however with some individuals coming in for criticism over their professionalism.
"We've got no divine right to come straight back up. We'll have to work hard," he said.
"I've inherited a group with some good professionals and also with people who are not so good. That has been the problem.
"Lots of them can't get up early enough to get to training on time.
"One player's picked up more fines than he earns and he earns enough."