The Cottagers more than held their own with the league leaders, but Wayne Rooney's delightful strike 11 minutes from time bagged all three points for the visitors.
Jol's men had their fair share of chances in an entertaining contest, and Fulham's display gave their manager cause for optimism.
"We did well in midfield and at the back," Jol said. "It was one of our better performances this season.
"But they are capable of creating something out of nothing, as Rooney did. Now, I think they will win it."
Fulham suffered an injury blow with the loss of key defender Brede Hangeland to an Achilles injury, but Jol added: "Hopefully it is not a long one."
The game was disrupted by a floodlight failure three minutes before half-time, although Jol felt the delay did not affect the outcome.
"We did well to get the lights on again," he said. "Normally it takes a long time.
"I feared when we came back our concentration was down and we would end up conceding a goal but it wasn't a problem."