The highly rated Dutch coach was a key member of the Manchester United backroom staff under Sir Alex Ferguson and his appointment represented quite a coup for the west Londoners.
The loss was the Whites' fifth on the bounce in all competitions and resulted in the bookmakers shortening odds on Jol becoming the next Premier League manager to leave his post.
The under-fire Dutchman felt the full force of Fulham supporters' anger on Saturday, trudging off to a chorus of "Jol out", yet he remains confident of turning things around alongside Meulensteen.
"Before the games against Man United, Liverpool and Southampton, we had a very good spell," Jol said.
"We played some good football against Stoke and Crystal Palace, we had a good tempo, a good rhythm.
"But after the three games and three defeats, he called me and told me that he would like to come.
"After a couple of tries, he said he would come and that is good because it is a different mouth.
"It gives you different things in training and on the pitch, but it is the same thing.
"He said he would like to get the best out of [Dimitar] Berbatov, for example, which is what I always try to do and it didn't pay off against Swansea. That's the only thing.
"You can't change the world in two weeks or one week."
The likes of Adel Taarabt and Kieron Richardson praised Fulham's decision to bring in Meulensteen before the match, while Jol said he masterminded the appointment after some suggested he is the club's manager in waiting.
The former Anzhi boss' appointment would certainly be welcomed by many Fulham fans, who not only turned on their manager against Swansea but also some players.
Bryan Ruiz, Jol's only big-money signing, took the brunt of the criticism and was jeered off the pitch when substituted for the second home match in a row.
The Costa Rica international made no mention of that reception after the match, saying those connected with Fulham "must not despair" and should keep a "cool head".
Despite such philosophical comments, Jol revealed the constant criticism is impacting Ruiz's confidence and pleaded with Fulham fans to lay off him.
"You will see in Brazil [at the World Cup] that Bryan is a very good player," Jol said. "But he needs a little bit of confidence and that is what I would like to tell the crowd.
"For me, I don't have to play but for him it is probably a problem if they get on his back and he can't produce what he is capable of."
Ruiz and his Fulham team-mates will get a chance to stop the rot when they travel to fellow strugglers West Ham next weekend.
Swansea, meanwhile, face an unenviable trip to title-chasing Manchester City after facing Spanish giants Valencia in the Europa League.
With such tough fixtures coming up, the 2-1 win at Fulham proved a timely boost for Michael Laudrup's side.
Swansea had not won for over a month before Saturday, when an Aaron Hughes own goal and Jonjo Shelvey strike ensured Scott Parker's fortuitous strike counted for nothing.
"We needed the three points," Shelvey, on as a second-half substitute, told Swans Player after his fantastic winner.
"It's important that we beat teams like Fulham because they are around us in the table. I think it will kickstart us for a good season now.
"I was disappointed not to start, but that's football. It was important to get on and show the manager why I think I should start."