Carragher: Liverpool didn't want me
Carragher represented the Merseyside club 737 times from 1996 to 2013, including 508 league appearances.
However, the one-club stalwart and local product was not asked to remain at the club in a coaching or advising role, and said he was "embarrassed" during his final season.
"I was never offered a role by someone else or at Liverpool," Carragher told The Anfield Wrap podcast.
"I told [manager] Brendan Rodgers 12 months before the end of that season that I was finishing. I knew I was finishing. I'd had enough of being a substitute.
"I said to Brendan 'I understand [Daniel] Agger and [Martin] Skrtel are your first choice, I want to help you as much as possible as a manager. I want to play, if I play well obviously I'd love to play, of course' and I got back into the team which was a brilliant ending for me.
"But he knew then that I was actually close to jacking it in halfway through the season just because I wasn't involved. I was embarrassed training every day."
And Carragher, now a pundit with Sky Sports, said his chances of returning to Anfield on a permanent basis were small.
"I don't think I'll ever move home, if I'm honest, so the chances of being a manager or a coach dwindle a bit there as I wouldn't be moving my family around this country, let alone Europe or whatever," he said.
"Who knows in the future but I'm enjoying what I'm doing."