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."
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."
Carragher will mark his lengthy tenure with the only club he has played for with a testimonial at Anfield on Saturday against an Everton XI.
He has persuaded a number of former Reds to turn out for his Liverpool side and the likes of Michael Owen, Danny Murphy, Jerzy Dudek, Luis Garcia, Emile Heskey will make an appearance.
There has been some speculation Owen's return, as he now plays for arch-rivals Manchester United, may not be a happy homecoming but Carragher said that would be unfair.
"I hope it doesn't affect the reception, I think he deserves a great one for what he did for Liverpool," said the centre-back.
"He was a fantastic player right up there with the greats for what he did.
"He left in difficult circumstances (Owen was sold to Real Madrid with less than a year remaining on his contract) but when he went to Manchester United his career was on a bit of a downward spiral, he'll admit that himself.
"The chance to go to one of the biggest clubs of the world was difficult to turn down.
"He moved and upset some people but he had to do what was right for himself and his family.
"His kids were just starting school and he wanted to move back home so that came into it as well.
"I saw the other day Bobby Charlton played in Tommy Smith's [testimonial] and he wore a Liverpool kit - I think that is worse isn't it?
"But it will be good for a lot of those players to get the appreciation of the crowd.
"If I was in that situation and moved away from Liverpool I'd love the chance to play at Anfield and pull on the red shirt again."