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.
"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."
He added: "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."
Carragher is confident the club's failure to sign a striker in the transfer window will not adversely affect their fortunes this season. Manager Roy Hodgson had said at the weekend finding a quality back-up for Fernando Torres would be "the icing on the cake" for his summer dealings but the deadline passed without a suitable reinforcement being secured.
Torres is obviously first-choice but is still working his way back to full fitness after two knee operations in the final four months of last season curtailed his domestic season and affected his performances as Spain won the World Cup.
The fitness of the 26-year-old, who has yet to get through an entire Liverpool season without any injury, is paramount to Liverpool but Carragher said it was not a concern Hodgson had not been able to bolster the forward line.
"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."