The sixth-placed Reds are seven points adrift of Chelsea, current occupiers of fourth spot and with a match in hand.
There are 27 points available to Rodgers' side in the remainder of the campaign, which theoretically allows them to reach 72 points.
With the requirement for attaining fourth place having reduced over the last couple of seasons - Tottenham finished with 69 last year compared to the 76 Liverpool required in 2007-08 - there still remains an outside chance.
And England captain Gerrard said: "Liverpool don't belong in seventh, eighth or ninth in the table. We want to push for the European places year after year.
"Hopefully it's not too late but we will need to produce the perfect finish to sneak in the back door.
"The top five places are the target. Let's see what happens in other big games that are not in our control.
"Hopefully the teams above us will slip up. All we can control is our performances and our consistency and hopefully we will finish strong."
Liverpool overcame a significant hurdle with the 3-2 defeat of Tottenham on Sunday, coming from behind for only the second time this season to beat a top-five side for the first time since Rodgers took over last summer.
"I think this season has been slightly strange in the way that usually we do really well against the top sides and we slip up against the sides we should be beating," added Gerrard.
"But we have been putting those sides away quite comfortably with three, four and five-nils and looking really good.
"We haven't got the points we've needed against the top sides.
"This result and performance will give us great confidence and belief.
"Hopefully it will be a springboard for us to go on and finish the season really strongly.
"At times we haven't got what we've deserved against top sides but we can't look for excuses.
"We are where we are and we need to take responsibility for where we are in the league."
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Premier League Top 4 Finish 12/13 Top 4 Finish: Liverpool 150/1
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