Goals from Damien Duff, Danny Murphy and Andrew Johnson earned the hosts a convincing victory at Craven Cottage in the first leg of their Europa League first qualifying round tie.
A further 22 matches remain if they want to repeat their 2010 heroics of making the final, but the west Londoners look in a strong position heading into next week's second leg at NSI.
The triumph was also the perfect start to recently-appointed manager Jol's tenure, but the former Tottenham boss was not getting carried away.
"If I say [it is job done], you will tell everyone I said the job was done so I will say it's a good score," he said.
"We started off brightly the first five minutes and then it was difficult to find the spare man up front.
"The second half was better. If there was no possibility to play it up to Andy or Bobby [Zamora] you have to play down the flanks and the second half was better."
Fulham dominated the game from start to finish and Jol admitted the only disappointing aspect of the evening was that they did not win by five or six goals, especially after naming the strongest possible starting line-up.
He had hinted that he would blood in youngsters during the early rounds but named Danny Murphy as skipper, while also picking the likes of Brede Hangeland, Bobby Zamora and Damien Duff.
Jol may deploy some youngsters for next week's away leg after the 3-0 win, but quashed fears over the detrimental effect of the long journey.
"If we were playing on Sunday, for example, it would be a problem, but we don't have another game for a week," he said.
"We will use a principle of tapering off, so we will meet again on Sunday - maybe Monday."
He added: "Bobby Zamora is fit but, of course, he is not completely fit.
"But I think 80 per cent of the players are not completely fit.
"But to be match fit now it will take a couple more weeks.
"It is possible that we may use some youngsters for the second leg."
Thursday night's game marked the start of an 11-month season for Jol and his troops, which some fear could see them struggle in the Barclays Premier League.
Some have also questioned the logic in starting the competitive season so early, but Jol took a philosophical view of it all.
"Yes [it is early] but on the other hand all the other teams will play their first friendly game soon," he said.
"You have to approach it as a serious game but if you play a friendly game you do that after six or seven days and that's exactly what we did today so I don't think it has a big difference."