The west London club have not won since the opening day of the season and were booed off the pitch on Saturday as they conceded another late goal, this time against Cardiff City
Jordon Mutch's stoppage-time strike secured a 2-1 win and three points for the visitors, with boos and chants of 'Jol Out' audible after the final whistle.
But the Dutch coach was keen not to blame his players for their poor form, which has seen them pick up just one point from their last seven home games, and has called for the club to keep faith in his abilities.
"I think if you look at other teams as well, if you are in the bottom three or bottom five, even if it is early in the season, you get pressure," said Jol after the match.
"I take responsibility, because I can't say the players don't work hard. They work hard, they try to win games, but it is not easy for us to win games.
"I will always be calm and I hate it when people are getting worried and nervous, especially if they ask a manager to quit - that is awful.
"You never know what will happen with a new manager, because if we are bottom of the table at the end of the season it is not about me because I won't be here, it's about the club and I do not want to see this club at the bottom of the table.
"I know we can do better."
Jol once again urged the Fulham fanbase to readjust their expectations - "Fulham are not a club who should be in the top six" - and called for patience as the Cottagers' new signings gel with each other.
"[The fans] expect us to do better," the 57-year-old continued. "If you look at the players, I think in our situation we did remarkably well to get [Darren] Bent, [Adel] Taarabt, [Dimitar] Berbatov, Bryan Ruiz.
"But now it's late September and we have to play together. Today again, there's too many things which are new to them. But I don't want to use that as an excuse."
Victorious manager Malky Mackay, meanwhile, was pleased with his side's performance on Saturday afternoon and felt they had merited all three points prior to Mutch's late winner.
"I was delighted with the way we played today, from the first minute to the last," said the Scot.
"We ended up with 24 attempts on goal and I think away from home that is a fantastic start. We had a lot of domination of the ball. Overall I think we deserved [to win]."