The 35-year-old is set to play his final game for his hometown side on Sunday against QPR following 17 seasons and 737 first-team outings for the Anfield club.
And Sir Alex, who is calling time on his managerial career after 26 years at Old Trafford, says Carragher is a model professional who he has great respect for.
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"He's been a bedrock of their defensive qualities for years and years. I loved him. He's a fantastic example for any young lad that wants to play the game. He's been a really, really good professional."
Carragher struggled for appearances in the first half of the campaign but has started 14 of Liverpool's last 16 Premier League games, and Sir Alex compared the centre-back to former United captain Steve Bruce.
"He's absolutely the type of player a manager wants," Sir Alex continued. "I used to rave about Brucie [Steve Bruce] and the nine years he had with us, and I think Jamie Carragher is that exact same mould - can play with injuries, gets knocked about and gets back up, hardly misses a game.
"You're lucky to have players like that. I was lucky to have Steve Bruce and he is the same type of player. A fantastic player."