The defender, who retires from football after facing Queens Park Rangers on Sunday, was ruled out of action for four months a decade ago after suffering a serious injury at Ewood Park.
Such was Carragher's determination to help the Reds, however, that the centre-back attempted to continue according to ex-teammate Murphy.
"You've got to say well done to him - to play that many games at one club and to be that successful and the amount of games he has played," said Murphy during a joint interview alongside Carragher on radio station talkSPORT.
"Avoiding injury is not just luck - it's desire to play. I remember him at Blackburn when Lucas Neill broke his leg and he actually tried to get back on the pitch with a broken leg. That's testament to him.
"He's just been a brilliant servant for the club and a great lad. Everybody who knows Jamie and has been around him doesn't say a bad word about him.
"We could all tell a few stories that might make you smile but ultimately he's a good lad. I've got nothing but fond memories of spending time with him and playing with him."
The pair excelled at Anfield during the reign of Gerard Houllier, helping the club to a treble of trophies in 2000-01. It's a period Murphy remembers with great fondness.
He added: "It was always a pleasure to play with him because he was firstly a mate and, secondly, we played together either on the right or the left a lot of the time.
"Houllier put some trust in us to stop the opposition. He always used to swap us about - even if Jamie ended up left-back or right-back, he seemed to put me in front of him.
"Because of his communication skills, he was always brilliant with me; keeping me in the right place and doing the right thing.
"What they'll miss the most about him when he's gone is that every player can be replaced to a point, but it's what he brings off the pitch - the mentality of knowing what that club means, what it's like to play for Liverpool and every single day on that training pitch getting the best out of others."
A new documentary featuring Jamie Carragher's managers, teammates and some high-profile opponents airs for the first time at 7pm BST on Friday, May 24 on LFC TV. 'Carragher' will also be available on LFC TV Online and will conclude a fortnight of tributes across club media.