Carragher: No chance of Liverpool title this season
A championship title, which Carragher has never won in his 14-year professional career at Anfield, will probably have to wait.
"People have said 'You've done this and that for Liverpool' but we've not won a trophy for four years and that is annoying me a little bit," said the 32-year-old defender.
"I certainly don't want to go on another couple of years not winning one before I finish at Liverpool.
"I don't see any reason why we can't win a trophy this season or the next couple.
"The one I haven't won is the league but I suppose that will be very difficult this season going from seventh last season.
"But I see no reason why we can't have a good go and have a trip to Wembley."
"If you take into account the changes at the club in the sports science department I think up to now we have done quite well at the start of the season with injuries," said the Reds vice-captain.
"We are looking for Fernando to stay as fit as possible but I think David Ngog in the last 12 months is a completely different player, and his start to the season has been fantastic.
"We've also got Dirk Kuyt and Ryan Babel as well."