A Fernando Amorebieta own goal was followed by strikes from Martin Skrtel and Luis Suarez as the Cottagers found themselves 3-0 down at the break.
Suarez added his second to make it eight in the league this season and had it not been for goalkeeper Maarten Stekelenburg the scoreline would have been a whole lot worse.
Fulham are 16th with only 10 points from 11 matches but Jol will defiantly soldier on despite increasing speculation about his position.
"I think every manager in every team in the bottom six or seven has to keep fighting," said the Fulham boss, who admitted he had not spoken to owner Shahid Khan about his future.
"At the end of the day, I think we will be fine. We have to suffer during these games.
"I think you have to be an expert if you are in the bottom four or five to keep teams up and I don't think there are a lot of experts.
"On the ball we looked okay for the first 20 minutes and then we conceded a goal from a set-piece, then a second from a set-piece and you make it too difficult to get a result.
"It's not acceptable. The only thing I say is you make it too difficult if you concede cheap goals like that against the top teams.
"I feel conceding goals from set-pieces, which is the easiest way to defend, is unacceptable.
"On the other hand, you see it happening all the time at clubs.
"It is a cliche to say you have to show character. You would like to stay in the dressing room but you can't so you have to go out there and try to do something.
"I feel that is what we did but it is not enough to get a result after being 3-0 down."
Liverpool manager Brendan Rodgers saw his side bounce back from last week's defeat at Arsenal, their second of the season, in resounding fashion.
"I thought we played very well. Our appetite for the game was outstanding," he said.
"We had a hunger to get the ball and we had more than 30 shots on goal, it was a real dominant performance, very pleasing."
The Reds boss also paid tribute to captain Steven Gerrard who, after being criticised for not being able to influence the game at Arsenal, had a hand in all four goals.
"Steven's delivery is as good as it gets. No-one delivers a ball like Steven Gerrard," he said.
"I felt that the other players were not utilising the quality we had in the team in his delivery and so I asked them to be more aggressive when they attack the ball and to get across their defender.
"Every week I tell him where I want him to put the ball and he puts it there.
"You saw with two of our goals - the free kick and the corner (for the own goal and Skrtel's header) - there was incredible quality on his deliveries."
Gerrard was restricted by a hip problem at the Emirates and he was withdrawn after 67 minutes with the game won against Fulham but Rodgers does not think it will be an issue for the forthcoming England internationals.
"He obviously has had an issue with his hip," he said.
"Where I can rest him I will and we obviously had enough control of the game to do that.
"I think he is obviously a modern, seasoned professional at the top level so where he can get those little breathers it is important to get them.
"I haven't spoken to the medical people but he should be fine."
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- Martin Skrtel
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