The midfielder is confident the Reds, who finished the season in style, can topple the likes of Arsenal and Tottenham to qualify for the Champions League
Brendan Rodgers' side finished 12 points off the Champions League spots last season, ending the campaign in seventh as they failed to qualify for European competition altogether.
However, Gerrard feels Liverpool, who lost just one of their last 13 games in 2012-13, can overhaul the likes of Arsenal and Tottenham and secure a place back among the continent's elite clubs.
"The final five or six months of the season were fantastic, we showed fantastic form - I think it was top-four form," Gerrard told the club's official website.
"We certainly finished the season really strong, but we were very inconsistent from August to Christmas - 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. 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, I believe we can push into the top four. That would be a fantastic achievement if you look at the standard of the teams in this league."
Gerrard is also quick to praise manager Rodgers, who he thinks is improving the team despite a slightly disappointing first season at Anfield.
He added: "I think the manager has done well - he's taken a huge job on at a young age.
"I think he's moving the team and the club forward and making good progress. If he gets the backing from the owners, and the current squad that we've already got improves, I'm sure we can make the fans happy."