The veteran centre-back captained his side to a win over Mansfield in the FA Cup, but knows he is likely to be back on the bench for Sunday's league game at Manchester United
The 34-year-old has been at the club since 1990 and is idolised by many Liverpool fans, but Carragher is fully aware that Martin Skrtel and Daniel Agger are the number one centre-backs at the club, and the former England international just wants to help out as much as he can.
"If I was in this situation 10 years ago or even four or five years ago then I would have left, there’s no doubt about that," he told the Daily Telegraph.
"But now, I’m coming towards the latter part of my career and I don’t want to cause a problem for my club. I’ve never even spoken to the manager [Rodgers] about my situation or said I want to play. I wouldn’t want to do that."
Although Carragher concedes he is likely to start on the bench for big games such as the Manchester United fixture on Sunday, he still feels he can offer Rodgers something when the manager needs his services.
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"I’ve had my go, the team wasn’t built around me but I was one of the main players," he continued. "It’s their team now and I help, that’s the way I look at it and I wouldn’t want to cause anyone at the club a problem or finish at the end of the season or the next 18 months with a cloud over me."
The vice-captain has racked up 720 first-team appearances for Liverpool since making his debut under Roy Evans' management in the 1996-97 season. He has taken time to adapt to life as a bit-part player, but he feels he has learnt valuable lessons under current boss Rodgers since the start of the season.
"Last season when I started to be sub a lot I was getting frustrated," Carragher reveals. "He told me 'there’s nothing worse than a bitter sub’ and that stayed with me. And what he meant is you still have to prepare properly. If you watch me, I’m always warming up, I don’t just sit on the bench. I could be on any minute. I do my running after the game, my massage before, my ice bath."
Liverpool have been in better form of late with three wins in their last four games after a disastrous start to the season, and a win at Old Trafford against Manchester United on Sunday would take them level on points with Arsenal in sixth place in the league.