The Reds defender is remaining patient after falling down the pecking order at Anfield and is optimistic about both his and the club’s future
The Bootle-born defender highlighted his desire to play but confirmed his understanding of manager Kenny Dalglish’s decisions.
"Of course, every player wants to play," he told reporters.
"But I went out of the team through injury and other players have come in and played well. The manager has been fair to those players and rightly so.”
Carragher also praised the form of the defensive pairing which have consigned him to the bench this campaign.
He continued: "Daniel Agger and Martin Skrtel have been two of our best players. I've got to wait my turn, just as other players had to wait their turn when I'd been playing for so long.”
The 34-year-old went on to laud the impact that Dalglish has had since his arrival and believes that this season can end their run without a trophy.
He added: "Obviously we had the ownership situation that got sorted out. Then Kenny came in, and we had massive upturn in form.
"When you're at Liverpool as a player or a manager it's about winning trophies and we're very close this season and desperate to go all the way in the FA Cup."
As well as domestic cup wins, Carragher says that the squad has eyes for Champions League qualification and believes it is attainable.
He said: "The top four is also a big ambition because, of course, the Champions League is a massive part of the game, and that is something we want to be a part of.
"The season's there for us, and if we can put a great run of form in between now and the end of the season we can achieve a lot."