The loss was Fulham's seventh in 11 league matches and leaves them only two places above the relegation zone.
Their performance was described as "gutless", "embarrassing" and "woeful" by their own fans on social media sites and, including the final eight matches of last season, Fulham have won only four of their last 19 league games since April.
Jol's position under the club's new owner Shahid Khan, who did not appoint the Dutchman, is looking increasingly tenuous especially as Saturday's match was virtually all over as a contest well before halftime.
Luis Suarez continued his blistering from by making it 3-0 in the 36th minute and adding the fourth in the 54th, and there was never a hint that Fulham, who have only won once at Anfield in 32 league and cup matches dating back to 1934, were going to salvage anything from the game.
"It was a difficult afternoon. After conceding the first two goals it was almost impossible to get back in the game," Jol told reporters.
"We were not good off the ball - they played around us and we needed more toughness and aggression, which is what we did in the second half.
"The second half was not enough - you can't start like that and concede goals like that. But we are still up for the fight."
Jol also bemoaned his side's inability to transfer what they do in training to the pitch.
"We do everything in training and then we make the same mistakes. It was very frustrating, not only for the fans but for me and the team. I've got ambition and a mentality to win."
He reserved special praise for Suarez, who has scored eight goals in six league games since returning from suspension.
"Our appetite for the game was outstanding. Luis Suarez is a star talent but his core ingredient is his workrate, which is something we're trying to have throughout the team," said Rodgers..
"He covers and presses and is a good talisman. Our quality was very good."
One man especially pleased by Liverpool's win was Hollywood actor Mike Myers, a die-hard Liverpool fan who said he was "speechless" for once before entertaining the Anfield crowd.
Canadian Myers, Dr Evil in the Austin Powers comedy film series, was guest of honour and added: "I think Liverpool have every chance of getting into that top four this year.
"When (Daniel) Sturridge and (Luis) Suarez get the ball you just don't know what's going to happen. It's old-school Liverpool," he said.
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