The 35-year-old centre-back on Thursday announced he would 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."
Although his playing days may be coming to an end Rodgers would like to keep a player whom he has used as a sounding board during his first season at Anfield close at hand, although Carragher has yet to decide where his future lies.
"It is something he has thought long and hard about over the last 18 months," said Rodgers.
"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 is too early to say but in relation to staying on it was always clear it was something I wanted Jamie to do."
While Rodgers will scour the transfer market for a replacement he has a couple of promising youngsters within the set-up in Martin Kelly, currently out with cruciate knee ligament injury but set to sign a new contract as early as next week, and Andre Wisdom.
"Martin has shown a commitment to our vision here. He is a young player who really impressed me when I came in," he said.
"He was exceptionally good in the games he played earlier in the season.
"Andre has played a lot of his career at centre-half but has also shown he can play in a couple of positions.
"It will be interesting to see over the coming years and time will tell as players will improve as they get older."
With Carragher announcing his impending retirement a sharper focus turns to the other half of the team's Scouse heartbeat Steven Gerrard.
The captain is two years younger (he turns 33 in May) but Rodgers believes he can go on for some time yet after putting in some stellar performances recently, having played every minute of every league match so far.
"He has been instrumental now for a number of months," he said.
"He is adapting and modifying his game but he still has the qualities he has always had.
"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.
"He was outstanding (for England) the other night playing in that slightly deeper, controlling role which I think he can play as the years go on.
"He is able to dictate the rhythm of the game and some of the invention and creativity in his passing was brilliant and defensively he was very good."
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