Brendan Rodgers' side came a disappointing seventh in the Premier League last term but they found some good form in the final few months to offer hope for the future.
Having lost just one of their last 12 matches, Gerrard is confident Liverpool can mount a strong challenge for the top four if they start off in the same vein.
"The final five or six months of last season we were fantastic, and we showed top-four form," Gerrard said in the Daily Star.
"But before then we were inconsistent from August to Christmas and that's the reason why we never managed to achieve what we set out to do, which was a top-four finish.
"But I felt at times in the season we played some brilliant football and if we can find that level on a consistent basis, I've got confidence we can break into the top four.
"The realistic message is to say to the fans that the last four or five months of the season were really positive, we played well.
"If the fans get behind us and show the support that we know they can, then I believe we can push into the top four.
"The final five or six months of last season we were fantastic, and we showed top-four form."
Gerrard acknowledges that Liverpool have an excellent opportunity to get off to a flying start, after the fixture list left them facing just one of the teams who finished above them in their opening nine games.
He said: "We have got to be reasonably pleased with the start we've got - but you need everyone to turn up and perform to their very best.
"I look at the fixtures all the time but the most important thing is to not get too carried away. This time we need to get off to a good start to the season and be positive for that first home game against Stoke."