First-half goals from Roberto Firmino and Mohamed Salah were enough for Liverpool to close to within two points of second place Manchester United, who were beaten 1-0 by Newcastle.
With Manchester City clear at the top of the table, the race to finish in the top four is hotting up with six points separating United and five placed Chelsea.
Arsenal have been cut adrift in sixth on 45 points but speaking after the match, Klopp said he felt the nine-point lead over the Gunners was not enough and called on his players to continue pushing.
Klopp said: ”It was not a brilliant performance, not everything worked quite well, the wind was quite strange.
“It was difficult circumstances and we did the job. That is very important.
“We scored early, got the second goal in the right moment and then controlled the game.
“We don’t have normal weekends anymore. We want to finish the season top four and we need the points.
“I don’t think nine points from Arsenal is enough to have rest but it is nine points.
“There is a lot to go for and we will try to carry on like today.”