Neither side were in particularly good form heading into the all-London clash, yet the inept Whites made Sam Allardyce's side look like world-beaters.
After a decent enough opening 45 minutes, Fulham's second-half display was abject and, in truth, they were fortunate to escape just 3-0 losers.
Mo Diame, Carlton Cole and Joe Cole struck for West Ham, with chants of 'Jol out' growing as the match wore to a close.
Shahid Khan has shown impressive patience during Fulham's poor start to his first season as owner, but one bookmaker now has given odds on Jol leaving by Monday of 11/4.
Asked if he was confident he would be in charge for Wednesday's home clash with former club Tottenham, the Dutchman, in charge since June 2011, said: "It is not in my hands.
"If I have to worry, I was probably worried a couple of months ago because it is not one day and then the other. It is probably the last two months we have been inconsistent.
"I think it has worked out for me [at Fulham]. We had over 100 points, probably more than West Ham, over the last couple of years - more than any other team in the bottom half of the table.
"But over the last couple of months I think sometimes we are not strong enough."
Jol admitted this is the worst run of his managerial career and leaves him as short as 1/8 to become the next Premier League manager to leave.
"I am someone with maybe 700, 800 or 900 games under my belt as a manager, 1,400 probably in total," he said.
"I know that three points can probably give you a total different view and a different world.
"This run is why we are in the bottom three because that will happen if you don't get the points.
"If we had beaten West Ham, they would probably be in the same situation.
"There are other teams [down there] and there will be other managers in the next couple of weeks [coming under pressure].
"But you need to get out of that situation and we didn't today. Again."
Jol hit the table at the end of his press conference, perhaps due to the frustrations of another poor performance from his side - pressures West Ham counterpart Allardyce knows all about.
"You cannot be in our game without feeling anything for each other when things are not going our way," the former Bolton, Newcastle and Blackburn manager said.
"It is a lonely old job when you are trying to find the right solution to poor results.
"It is one where people don't really understand what you go through because they have never experienced it.
"Only talking to ourselves and pulling ourselves through, and obviously the people that you interact with on a regular basis, can help.
"You're in a position where you take all the heat and you've got to take all the heat because it is your job.
"If it is going bad, it is your responsibility no matter whether you've got injuries, no matter whether you should have signed this one or that one before the deadline.
"It is no excuse in the end, even though it is an excuse for not getting the result everybody expects."
The result leaves Fulham three points off safety and impressively ends West Ham's miserable five-match winless run in the league - even if it took the late introductions of both Coles for the match to be tied up.
"The only disappointing thing was that we didn't score more goals before the subs came on," Allardyce added.
"That was something I was getting pretty nervous about at 1-0, knowing Fulham could capitalise on a mistake and perhaps get something they didn't deserve.
"We had many chances to go 2-0 up before the subs came on, but when they came on and finished it off it is just great for you as a manager. Finally, you've got the victory you have been searching for."
Source: PA
Source: PA