Veteran defender Carragher, who will retire at the end of the season, has made over 700 appearances for the Reds since his debut in 1997.
Reflecting on Carragher's contribution, Spaniard Enrique has insisted that the centre-back has set an "example" for all the other players at Anfield.
"You have to respect the past he has here. He's a player that has played 700 games," he told the club's official website. "It's not lucky, he deserves it. He has been an amazing player for Liverpool for many years and he's an example for any player here."
Enrique went on to confess that Carragher's presence was one of the factors behind his decision to join the club from Newcastle United in 2011.
"One of the reasons I came here was Jamie Carragher, Steven Gerrard and now Luis Suarez," he added. "These are players that have amazing history at the club and I want to try to be like them in the future here.
"It was one of the best decisions in my life, in terms of football. Of course, I already played for a good club at Newcastle, but you can't compare one club with the other in terms of history."
It was confirmed earlier today that Carragher will join Sky Sports as a pundit from next season.