Fulham headed into Monday night's London derby at Selhurst Park with just two wins from their opening seven Premier League games.
Reports had suggested that Jol was under pressure but, after Adrian Mariappa had put Palace in front, Kasami's majestic volley sparked a Fulham comeback which delivered a comfortable victory.
"It was unbelievably important to get a result and, of course, for them it was a game of importance," Jol told Sky Sports.
"We were on seven points and you get under pressure like all the other teams on seven, eight points, so we needed the three points and now we're in a better position for Fulham.
"The media will build it up, but I love to have some pressure and the boys will feel the same. They want to do well for me and the club, and that's what we showed. Everybody is happy again.
"You want 20 points first, then 30 and 40, which is not easy in this league, but I feel we've got the players to do well and I think we're in a better position now."
Jol was also delighted with Kasami's goal after the winger brought Sascha Riether's pass under control on his chest before arrowing a volley over Julian Speroni.
The Fulham boss added: "It was a fantastic Kasami goal, with his wrong foot. It was unbelievable because I haven't seen him do it before.
"I think it's probably better than people feel or think because he had to control the ball on his chest, then with his wrong foot in the other corner. It was a real good goal from a talented boy."
Regarding comparisons to Van Basten's volley for Holland in the 1988 European Championship final, Jol said: "That was totally different, you can't compare the two, but this was better!
"With Van Basten, that was one touch, but I think he (Kasami) sprinted 30 yards, then controlled the ball and to score the goal like that was probably even better. It could be one of the goals of the season."