Fulham's form has been frustratingly inconsistent this season, putting pressure on Jol after a run that has seen them slip to 16th in the Premier League, just two points above the relegation zone.
An opening-day victory over Sunderland was followed by a five-game run without a win, and although they won twice in October, Fulham have since lost their last three matches in all competitions.
They found themselves 3-0 behind against Manchester United inside just 22 minutes on Saturday, leading to sections of the club's support voicing their frustrations at the team.
But Jol has called on everyone to pull together to help them reverse their slide ahead of Saturday's trip to high-flying Liverpool.
"If they (the fans) are disappointed I can understand that," he said. "As long as we don't have the results they can do it (be disappointed) with me, but hopefully they will support our team because we are not in the best of situations, but not in the worst.
"We look for a few results. You have to start somewhere to get wins under your belt and then go from there. We need a few surprise results and maybe we can start against Liverpool."
Jol is also looking to move on from the controversy surrounding Sascha Riether's stamp on Adnan Januzaj at the end of the defeat against United.
Riether was not punished by the referee at the time but has since received a three-match ban after being charged retrospectively by the Football Association.
"If he did do it deliberately, it's fair enough he got three games," Jol admitted.
"The referee didn't see it, I didn't see it but they decided to give him that punishment.
"He apologised to the club, to the fans, to us, of course, and it's not what you need but we move on."
