The Reds moved within one point of fourth-placed Manchester United and third-placed Newcastle with a big win over Leicester on Monday night.
Curtis Jones bagged a brace at the King Power Stadium before Trent Alexander-Arnold scored a screamer to make it six consecutive wins.
After such a disappointing season, Liverpool are finishing the campaign strongly and could yet overtake either United or Newcastle in the final stages.
They host in-form Aston Villa on Saturday before finishing the season with a trip to a Southampton team who have already been relegated.
Still, Klopp insists Liverpool remain outsiders in the hunt even despite their relentless run of victories.
“It’s all we can do. I don’t think it’s likely [finishing in the top four] when you see how Newcastle and United play, they have so much quality,” he told Sky Sports.
“It would be a real shame if they slip and we’re not there. So we have to do our job.”