A third straight setback, and a seventh in 10 Premier League outings this season, has seen pressure mount on the shoulders of Cottagers boss Jol.
His side remain just above the drop zone, with there little margin for error in their bid to steer clear of a basement battle.
If they are to preserve their top-flight status, they will need to fare considerably better than they did at Anfield.
Liverpool's opening two goals both came from dead-ball situations, and Jol admitted afterwards that his out-of-sorts side had shot themselves in the foot.
He told Sky Sports: "It was a difficult afternoon. Goals change games.
"For the first few minutes on the ball, I thought we were okay. Then to concede two goals from set-pieces, that is what you shouldn't do against a team like Liverpool. We had a mountain to climb and Liverpool were the better team.
"After we had conceded the first two goals, it was almost impossible to get a result."
It is being suggested that Jol's days at Craven Cottage may be numbered, and he admits there are few positives he can take from another disappointing display on the road.
He added: "That's the problem when you play against the top three, top four. The only thing you can say is, get these games out of the way and try to get a result.
"But if you concede goals like that here you are never going to get a good result against a team like Liverpool."
Pressed on whether he still has the stomach for a fight, Jol said: "We're still up for the fight, yeah."