The west Londoners slipped to a fourth straight defeat thanks to an own goal from Aaron Hughes and a late Jonjo Shelvey winner, but their boss feels the margins of error are fine
An own goal from Aaron Hughes was cancelled out by a cross-cum-shot from captain Scott Parker as the hosts fought back, but Jonjo Shelvey's 80th-minute curler condemned the Cottagers to another loss.
Fulham were improved from previous displays, which has given Jol hope, but he admits his side are showing relegation-threatening form.
"Four defeats in the league on the trot is terrible, so it was evident today we needed the points," he told reporters.
"We need points, we need wins, but in the first half we were good enough to score three goals.
"Swansea would have been below us if we had the win today, that's the different between success and failure."
Rene Meulensteen was recently appointed as the club's new head coach, and Jol is confident his presence can improve the squad - namely former Manchester United striker Dimitar Berbatov.
He continued: "It's a different mouth and different things in training. He says he wants to get the best out of Berbatov, but you can't change the world in one week.
"I know these players, they know me, there is no problem in the dressing room. We need 40 points.
Swansea boss Michael Laudrup, meanwhile, commiserated with Jol's plight but also feels Meulensteen will only positive affect the struggling London side.
He added: "I feel sorry as we all have difficult moments, and a lot of times the finger is pointed at the manager. It's easier to change one than change 10, 15 or 20.
"I think anyone who has worked for Manchester United, and for Sir Alex Ferguson for so many years, must be [doing something right]."