Jurgen Klopp called for Liverpool to be "a pain in the backside" for the teams at the Premier League summit after the Reds beat Aston Villa 3-1 on the competition's return on Monday.
Liverpool cut the gap to fourth-placed Tottenham to five points by winning an entertaining affair at Villa Park, as Mohamed Salah, Virgil van Dijk and Stefan Bajcetic netted.
While Klopp concedes the 15-point gap which separates Liverpool from leaders Arsenal may be insurmountable, he says their primary focus is to put pressure on the league's top four.
"Look, we have to be a pain in the backside for everybody. That's how it is. Of course, we have to chase," he said at Monday's post-match press conference.
"We are not in the best position, there's a difference between us and other teams, we all know that. The first two [or] three are maybe too far away. If they win all the games, then we have no chance.
"We have to do our part, we have to do our part and that means winning football games and we will see how close we can get."
Liverpool have never failed to finish in the top four during Klopp's six full seasons in charge, and while the German accepts some of the teams above them have enjoyed terrific campaigns, he remains hopeful regarding their chances of catching them.
"Of course, it must be the target to qualify for the Champions League, and for that we have a lot of games to go for and we all have to go through difficult moments in games, between games, after games, all these kind of things," Klopp added.
"For today, we got three points and that's the best way to get closer to these spots. Of course, we go for that, there's no doubt about it.
"All the teams up there played an exceptional season, but as long as we can see them, we will fight for getting it. That's it."
Liverpool's opening goal saw Salah convert a low cross from Andrew Robertson, who was picked out by an outstanding pass from fellow full-back Trent Alexander-Arnold.
The right-back only played 33 minutes at the World Cup, but Klopp said there was no need for his staff to pick him up after his disappointing campaign in Qatar.
"I think with Trent, everything is fine. I don't think he expected to make all the games in the World Cup with all the players Gareth [Southgate] has available," Klopp said.
"He was there for his country and contributed as well as he could. He didn't like to not play, but he was not especially down and we had to pick him up, the situation was pretty clear and that's fine.
"Now he came back and got ill, that's not cool, that's why he couldn't play at [Manchester] City. And now he was available, but for him it was especially hard."