Fulham took the lead at Old Trafford through Damien Duff's early opener but were pegged back by goals from Robin van Persie, Shinji Kagawa and Rafael.
After the break, though, United's defensive frailties came back to haunt them, with David de Gea getting in a real mess trying to clear a routine cross, which ended with Nemanja Vidic putting the ball into his own net.
Unfortunately for the visitors, it was too little, too late.
After the game Jol expressed concern at the plight of Dempsey, who was again missing after spending the last five weeks training with the Fulham physios as he hankers after a move to Liverpool.
"Everyone thinks he was left out of the squad today but he has not been there for four or five weeks," said Jol.
"If there is no bid - like Steven Fletcher and Matt Jarvis at Wolves - he could have played until he got his big move. I would have liked that.
"But there is no official bid. It is a very bad situation for us, and for him of course."
And Jol wonders if something will happen before the transfer window closes on Friday to save him dealing with a very difficult situation.
"I am not a person who will not forgive a player," he said.
"I loved him last year but I have not seen him much this year.
"If there is no bid what can I do? I cannot sell him to the non-league or put him on loan at Stevenage.
"Maybe something will happen next week.
"He really thought he would be on the move four or five weeks ago. His head was turned.
"He thought it would happen in the next couple of days and it didn't."
Meanwhile, Jol admitted he was surprised at Wayne Rooney's absence from United's starting line-up.
"I was surprised," he said. "I thought Van Persie and Rooney would play.
"I know Kagawa from my time in Germany and I knew he would not play on the left. I thought it might have been an advantage because my players did not know him.
"He is a quality player. But Rooney is a fantastic player as well."
