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, in an LFC magazine interview, showed 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."
And 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 again.
"We can't keep talking about next season all the time. There are only so many times you can say it and believe it. 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.
Gerrard also expresses a disappointment that a season of crisis off the pitch has given "those in the media who don't like Liverpool" the chance to criticise.
"We have made it easy for them," he said.
"It's not been a good situation (the takeover speculation) for anybody. It's sad so much of the club's business has been conducted in public. The club I have grown up supporting always did its business behind closed doors, and that is what we have to get back to.
"It's been a damaging situation for every single person involved with the club, fans, players, bosses, owners, from top to bottom."
But Gerrard's theme, which should not be ignored by those "bosses and owners", is the lack of a real title challenge.
He added: "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.