Carragher, 35, announced on Thursday that he intends to retire from football at the end of the season, after more than 16 years playing top-flight football for the Anfield club.
"He's a real iconic player for this club and, for me, one which will be irreplaceable," Rodgers said.
"I don't think he can be replaced. I genuinely think he's a player who I would call a pure defender."
Carragher has of late been returned to the heart of Liverpool's defence, after concerns about a lack of leadership on the pitch.
Jamie is an outstanding leader and organiser in the team and to find someone with all those capabilities, and who has the heart the size of a lion, is very difficult.
And Rodgers has made it clear that he has depended on the Liverpudlian since taking up the reins at the club - even talking him out of quitting last summer.
He revealed he has also spoken to him about possibilities regarding a future with Liverpool in a non-playing capacity.
"It is something he has thought long and hard about over the last 18 months," Rodgers said.
"He had thought about his last summer when I first came in and we had some good conversations and persuaded him to stay on.
"From now until the end of the season, he just wants to concentrate on his football - beyond that, it's too early to say."
While the other half of the Liverpool 'Scouse heatbeat', Steven Gerrard, is just two years younger than Carragher, Rodgers isn't thinking about losing his captain to retirement any time soon.
"He is adapting and modifying his game, but he still has the qualities he has always had," he said
"This is a guy who has everything in the locker. A wonderful professional, a great man off the field - a real inspiration for any young player - who leads his life the right way.
"You see him on the field ... His range of passing, his touch, and his leadership qualities and his influence is getting stronger for me."