The 35-year-old centre-back has announced he will retire from football at the end of the season after more than 16 years in the Reds first team.
Rodgers has only recently brought the former England international back into the heart of the defence at the expense of Martin Skrtel after concerns a lack of leadership was being exposed.
The Reds boss claims Carragher was thinking about quitting last summer but was persuaded to carry on. Now the Northern Irishman has just a few months to find alternatives to the man he called a Liverpool icon.
"He has been a giant for me since I came in here, an incredible man, he is one of a dying breed," he said.
"He is someone who has good real old school values and ethics but, as you can see from his last two performances, he still has the qualities to play at this level.
"He is a real iconic player for this club and, for me, one which will be irreplaceable. I don't think he can be replaced. I genuinely think he is a player who I would call a pure defender.
"You see a lot of rash defending nowadays but he defends with great intelligence, he knows when to mark a man and when to mark space and understands the basic principles of defending.
"He is an outstanding leader and organiser in the team and to find someone with all those capabilities and has the heart the size of a lion is very difficult.
"That type you won't find but you have to look for other types with other qualities and that is something we will have to do."