The Cottagers lost 1-0 to Arsenal with Per Mertesacker scoring on the stroke of half-time.
Despite playing for over 80 minutes with just ten-men due to Steve Sidwell's red card Fulham could easily have taken something from the game.
Olivier Giroud also saw red late on and Jol feels both could easily have been bookings.
"I would not have given it, but I am his manager,"Jol told Sky Sports of Sidwell's dismissal.
"I am 100 per cent certain it was mistimed and he did not do it on purpose but he caught the guy. It was not his intention but as I said it was mistimed. If he had booked him and the same with Giroud I would have taken that.
"It is disappointing but he should not sell himself, he should stay on his feet. It was not the most intelligent thing to do and he knows that but on the other hand it was the first foul of the game and he could maybe have stayed on.
"But I have to say that after that incident we fought like lions and we had better chances than them on the break. Our shape was good and we played well and they scored just before half-time.
"We kept it 1-0 until the end and then we swapped Petric on and had a couple of opportunities to score and equalise. That would have been perfect and I could not ask for more.
"It was our third game in six days and we played with ten men for 83 minutes, but we stuck to it and showed a lot of character and in the end we could have had a result."
Jol admits that his side were disappointed not to have taken something from the game.
"I really thought we did very well and it is disappointing to play for 83-minutes with ten men but I said to them in the dressing room we fought like lions and we could have had a result. A draw would have been deserved."
Jol was not happy with the goal, concluding: "Organisation was not good, sometimes from all these changes you get this."