Carragher, who is set to retire at the end of the season to pursue a career as a football pundit, has been with the Anfield outfit for his entire career, making his debut in 1996.
And Enrique has revealed that both Carragher and fellow Reds veteran Steven Gerrard played a huge part in his decision to join the club from Newcastle back in 2011.
|11/4||Liverpool are 11/4 with Paddy Power to finish in the top six
"These are players that have amazing history at the club and I want to try to be like them in the future here.
"You have to respect the past he [Carragher] has here - he's a player that has played 700 games.
"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."
With his second season at the club coming to a close, the 27-year-old is delighted with life at Anfield, adding: "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 really quick; I knew there was interest from before the summer. When they started talking to Newcastle about how much I was going to go for, it was one or two days to sort it out. I told them I wanted to come here.
"I'm really happy with my decision to be here; it's my second season and I'm playing a lot, like last year. I'm improving a lot as a player and a person as well."