The 34-year-old has made nine appearances for the Reds this season in the Premier League, but the former England international has only started once.
With Daniel Agger and Martin Skrtel now Liverpool’s undisputed first-choice centre-half pairing, Carragher’s future at the club has been a source of speculation.
However, Rodgers maintains the Champions League winner still has a role to play, particularly off the field in terms of helping the club’s youngsters to progress.
“He’s unbelievable,” Rodgers told Liverpool’s website.
“I’ve been fortunate enough to work with top European players in my time. The will and desire of this guy is remarkable. I love every minute of working with him.
“It has not been easy for him [not playing in every game], but he’s from the old school. He’s got values and ethics. We communicate a lot, talk about football and life in general.
“He is always there for me to rely on with his experience of the club. He turns out every day and I’m sure there are days that are difficult for him, when he doesn’t play.
“Jamie and Steven Gerrard have been the best players here over a long period. Perhaps over a year to 18 months he hasn’t played as many games as he would have liked.
“I recognise his qualities on the field but, equally important, I recognise him as a man off the field. I hope he feels very much part of the family we have here.
“He is a wonderful example to any player, absolutely incredible. He has still got a few years left in him for sure.”