The 34-year-old vice-captain, who played in his fourth League Cup final in Sunday's Carling Cup win over Cardiff, wants the Reds to find the consistency to qualify for Europe on a regular basis - and he does not mean the second-tier competition.
"I think we are bigger than that," said the veteran centre-back. "We should be looking to get into Europe every year through our league position rather than through winning the Carling Cup.
"Yes, it is nice to have it in the bag but we are bigger and better than that.
"The next step is trying to get back into the Champions League.
"We know it is going to be a difficult task and obviously we have got a big game coming up against Arsenal this weekend.
"They will be flying after the win over Tottenham (when they came from 2-0 down to win 5-2).
"But getting back into the Champions League has got to be the next step for this club.
"Europe is part of our heritage and we need to be involved again."
Carragher admits winning the Carling Cup was a relief for himself and Steven Gerrard in particular.
The Scouse pair have been at the club since they were schoolboys and, with them both in their early to mid-30s, they were keen not to allow the chance to end a six-year trophy drought slip through their fingers.
"We're coming to the latter stages of our career, myself and Stevie, and because we have gone so long without winning anything you don't want to finish your career going seven or eight years without," he told talkSPORT.
"It was a relief for both of us to get a trophy, for ourselves and the club.
"It maybe takes the pressure off now for the next year or two and we can relax and go on to try to win more trophies, hopefully bigger trophies."
next season