The Reds finished seventh in the Premier League last season.
“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 Carragher.
“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.”
