The Liverpool skipper accepts that only fourth place now is acceptable as they battle to secure entry into Europe’s elite competition next term.
But he said: “You don’t get any prizes in football for finishing in second place, never mind fourth.
“I don’t think that the fans would accept fourth as an accomplishment and for me, it’s not nearly good enough.
“We need to improve dramatically and even if we do finish fourth, it doesn’t mean we have had a good season.”
Gerrard accepts Liverpool are now involved in a battle for fourth spot with Everton and Aston Villa, Portsmouth and Manchester City.
Having regained fourth place on Saturday by beating Middlesbrough, they saw Everton grab it back on Monday with an impressive demolition of Sven-Goran Eriksson’s City.
And the battle will rage on this weekend with Liverpool at Bolton on Sunday while Everton are at home to Pompey later in the day.
Gerrard has revealed his own frustrations and anger at the club’s current fortunes.
He said: “In the position we find ourselves now, fourth is the least that is acceptable. But we have bigger ambitions than that.
“The only way we can fulfil those ambitions is in the Champions League. And I am not going to pretend that even winning that trophy — and we are a long way away from it at the moment — will make up for the disappointment of the league campaign.
“I’m pretty gutted every time I look at the table and see the gap between us and Arsenal at the top, and even the gap between us and second and third.
“We believed we had the players to challenge for the title, and we wanted that one more than any other trophy available to us. I still believe we have the squad to be a hell of a lot more competitive than we are right now.”
Gerrard, significantly, claims the time has come for the club to stop looking at their long-term potential. The Reds skipper, who has again been linked recently with a summer move to Real Madrid, said: “I’m getting tired of saying the same thing over and over. We can’t keep talking about next season. Sooner or later we have to make one season the season we make it happen and do the talking on the pitch.
“We need to make people believe it. I’m 27 now, I don’t want to be talking about ‘next season’ for Liverpool when I’m 32.
“We’ve got the stadium, the fans, the manager and the players to compete for the Premier League. But we have no chance of doing that if we are always well out of it by the first week in January.
“And at the moment we have our work cut out fighting it out with Villa, Everton and Manchester City for fourth.
“If you asked most of our fans, they would rather see the title than the European Cup at Anfield. We’ve not won it in a long, long time.
“Looking at the league table hurts. This time last year we were third and Arsenal were fourth, and that is the way the season ended. It hurts to see where Arsenal are now.”
Meanwhile Dubai International Capital are believed to be considering making an offer for George Gillett’s half of Liverpool after co-owner Tom Hicks insisted he had no plans to sell his stake in the club.
Texan billionaire Hicks claims he is completely committed to the Reds and has denied reports he has invited DIC to inspect the club’s accounts in preparation for a takeover.
But while DIC would be interested in buying out Gillett instead, they would also want some of Hicks’ holding so they had the controlling interest in the club.