The center back announced his decision to call time on his playing career on Thursday, and is set to leave as the club's second-highest appearance maker of all-time.
And Rodgers, who has recently reinstated the Bootle-born defender to his starting XI, believes Carragher's qualities will be sorely missed.
"For me, he'll be irreplaceable. I don't think that type can been replaced," the Reds coach told reporters. "In the modern game there are very few like him. You see a lot of rash defending now throughout the game. This is a guy who's a pure defender, he defends with great intelligence. He knows when to mark a man, when to mark the space. He understands the basic principles of defending.
"He's an outstanding leader and organizer in the team, and to find someone with all those capabilities and who has got the heart the size of a lion, is very, very difficult to find. You won't find that type [anymore]. You obviously have to look for other types of players with other qualities, and that's what we'll have to do."
The Northern Irishman also revealed that he had attempted to persuade Carragher to postpone his retirement for another season.
"I've had many conversations with Jamie this season so I knew all along what was in his mind. He's obviously thought long and hard about it over the last 18 months," he added. "In terms of staying on it was clear that it was something I wanted him to do. Jamie had thought about this last summer.
"I came in and we had some good conversations and I persuaded him to stay on. He's been a giant for me since I've come in here. An incredible man and one of a dying breed. Someone who's got real old-school values and ethics.
"As you can see from his last performances in two big games, he's still got the qualities to play at this level. He's put his body through a lot over the course of these last 18 years and he's got a beautiful young family he may want to spend some time with.
"The supporters should really enjoy watching him because he's a real iconic player for this club."
The 40-year-old went on to admit that he is unsure what Carragher will do next, with the defender having seemingly ruled out an immediate switch to coaching.
"From now until the end of the season he just wants to concentrate on his football and doesn't want to look too much into the future," he continued. He's still very fit. He's 35 years of age but how committed he is to football has allowed him to stay in peak condition.
"At the moment he's only concentrating on doing everything he can to finish the season as a success. Beyond that, it's too early to say."
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