Jordon Mutch's stoppage-time strike earned Cardiff a first away win since their top-flight return and there were jeers directed at Jol at the final whistle.
Fulham have one point from their last seven home matches in the Barclays Premier League and their next opportunity to win at Craven Cottage will come against Stoke - managed by Jol's predecessor Mark Hughes - next Saturday, when six months will have elapsed since their last home success in the league, the April 1 defeat of QPR.
"I'll always be calm, but I hate it when people are getting worried and nervous, especially when they ask a manager to quit," Jol said.
"That is awful, because you never know what will happen with a new manager.
"If we are bottom of the table at the end of the season it's not about me, because I won't be here, it's about the club and I don't want to see this club at the bottom of the table.
"They (the fans) expect us to do better.
"If you are in the bottom three or bottom five, even if it's early in the season, you get pressure.
"I take responsibility, because I can't say that the players don't work hard."
He added: "Fulham is not a club who should be in the top six. We were 20th in the league in spending money."
Source: PA
Source: PA