Eberechi Eze scored the only goal of the game in the 14th minute to leave Jurgen Klopp's side third on 71 points, level with second-placed Arsenal, who were stunned 2-0 at home by Aston Villa.
Manchester City lead on 73 points with six games left.
Liverpool, who were held 2-2 by Manchester United in their previous league game, also face an uphill task in the Europa League after losing the first leg of their quarter-final against Atalanta 3-0 at home.
"We need to be perfect from here on in, for sure," Robertson told reporters. "We can't drop any more points and let's see what the other two teams (Manchester City and Arsenal) do. We have to stay positive. We don't stop fighting.
"We have to pick everyone up in the changing room because there's a lot of people who are down, whether they missed a chance, gave the ball away or whatever it is. We pick up, we go again on Thursday and we give everything we've got."
Liverpool next travel to face Atalanta on Thursday before returning to league action against Fulham.
