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.
"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."
It is not unusual for Fulham to be scrapping at the foot of the standings, Jol said.
He added: "Fulham is not a club who should be in the top six. We were 20th in the league in spending money."
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