The Dutchman believes that referee Mark Halsey was wrong to award the Black Cats a penalty in the second half, a decision he insists changed the outcome of the match.
"In hindsight we controlled the first half but of course the penalty situation changed the course of the game. After that Sunderland smelt blood and had their confidence back," BBC Sport quotes Jol as saying.
"But I still feel it wasn't a penalty kick. If you give that, you have to give four or five in every game."
Jol went on to say that Fulham were the better team, particularly in the first half, and insisted they should have taken all three points.
"Don't forget, we should have made it 3-1 and put it to bed. We did ever so well in the first half, we controlled the game and dominated them. I'm not happy with one point," he added.
"We were the better team, it should have been a win. All these teams look behind them [in the table], everyone could be dragged into it."