Liverpool have also failed to score at home since their 4-1 defeat at the hands of Manchester City last month.
The result means that Jurgen Klopp’s side remain four points of the top four places while Fulham go level on points with 16th-placed Brighton.
Despite Klopp saying he wouldn’t turn his attention away from the Premier League, Liverpool made seven changes for the game ahead of their Champions League clash against RB Leipzig on Wednesday.
Fulham took a deserved lead on the stroke of half time when Andy Robertson failed to clear a corner and Lemina stole the ball off Salah on the edge of the box and produced a low shot into the corner.
Substitute Sadio Mane also came close to scoring after 70 minutes but his looping header clipped the post.
Liverpool pushed for a late goal but Fulham held on to secure an important win in their bid to remain in the league.