Liverpool boss Brendan Rodgers admits Manchester City, Arsenal and Manchester United are favourites to finish in the top four.
The Reds face a tricky away game against Hull City on Tuesday night with the Tigers involved in a relegation battle with Leicester City and Sunderland at the bottom of the table.
But the Northern Irishman says his players will keep fighting until the very end after setting "new goals" for the rest of the season.
"It will be a tough game away at Hull, they had a good result at the weekend," Rodgers said on Monday.
"For us, the idea is to go in and see if we can get the victory and just keep putting as much pressure as we possibly can on the teams above.
"It's a difficult game. We had a disappointing performance there last year; they are a good side with good players, they are a threat with the two boys up front.
"They play 3-5-2 and there's not a lot of space in the final third, so you've got to be patient to break them down.
"Obviously they have got good passers in midfield with Tom Huddlestone, who is a wonderful passer of the ball. So we respect them and know that it will be a difficult game.
"We have set new goals for the remainder of the season. It's really focusing on our performance level in order for us to win.
"If we can win the games, then that will automatically put pressure on. The teams above us obviously have the clear advantage, but you can only affect that by winning games.
"That will be our idea, starting tomorrow evening. If we can do that, it gets [the gap] down to four points.
"Manchester United have got West Brom at the weekend, we have seen how difficult it can be to play against Tony's team. We can only really focus on ourselves.
"But as we saw last year, lots of changes can take place in the last five games or so. We just have to be prepared to give everything to finish as high as we can."