Carragher has never won the title in his 14-years
professional career with Liverpool.
Defender Jamie Carragher accepts Liverpool's best chance
of silverware this season will come in cup competitions as they
have too much ground to make up on the likes of title-contenders
Chelsea and Manchester United.
The Reds slipped to their lowest Barclays Premier League finish
- seventh - for a decade last season.
With increased pressure from big-spending Manchester City this
campaign their priority has to be securing a place in the top four
to get them back into the Champions League.
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.
"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."