The Reds are seventh in the league table following a 2-1 win at Aston Villa last weekend.
Gerrard believes that Liverpool have shown glimpses of progression this season and will be serious contenders for Champions League qualification next year.
He told The Sun: "We've played well enough in the majority of the games to be higher, but when you look at performances like Southampton, Villa at home, West Brom away, Arsenal at home, there's a handful when this team hasn't turned up.
"That's the reason why we are sitting where we are in the table. We need to put the pressure on other teams for that European place. Especially as a lot of the teams above us still have to play each other. We're hoping there are a few slip-ups above us and we can capitalise on that. It's important that we take maximum points.
"We need to use the Villa game as a level from which to continue, because I thought our second-half performance was perfect, not just offensively but defensively as well. We know we aren't far away, and there will be improvements to the squad in the summer. We believe we can put in a better challenge for the top four next season."
Liverpool are currently five points behind fifth-placed Arsenal in the final Europa League qualifying place.