Despite Bryan Ruiz's equaliser just before half time, Fulham were unable to build on that and went down 2-1 in their Premier League clash at Craven Cottage.
The defeat leaves Fulham in 18th place in the league.
Jol told BBC Sport: "We worked hard but we didn't have the rub of the green. I'll always be calm and I hate it when people are getting worried and nervous. I think it is awful when people ask a manager to quit.
"I don't want to see this club be at the bottom of the table. I know we can do a lot better. I think we will be OK but this is a blow. Cardiff are not a team that are going to be in the top six and we have to win these games."
Fulham face Stoke City at home in their next league fixture.