The manager hailed the 35-year-old's contribution in his last campaign and believes it will be hard to fill the void he leaves after winning 12 trophies over 17 seasons at Anfield
The 35-year-old received a guard of honour as he entered the pitch with his two children in his final match as a player on Sunday as the Reds dispatched QPR 1-0 thanks to Philippe Coutinho's first-half goal.
The defender made his debut in 1997 and went on to make 738 appearances over 17 seasons for Liverpool, winning five domestic cups and four European trophies - including the Champions League in 2005.
|7/4||Liverpool are 7/4 with BetVictor to finish in the top four next season
"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."
Carragher struggled to get into Rodgers' first-team plans early on in the season, but has started every single game since the 2-2 draw with Arsenal in January and the manager hailed the veteran's level of performance to the end.
"He's an incredible player and a real gentleman," he continued. "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."