The Cottagers secured their first win in eight games to end their season on a high, as Swansea's memorable campaign ended with a whimper at the Liberty Stadium.
The excellent Alexander Kacaniklic put Jol's side ahead after 22 minutes, with Dimitar Berbatov and Urby Emanuelson sealing the victory late on.
But it could have been a very different result had Schwarzer not pulled off a string of fine saves as Swansea piled on the pressure in the second half with the score at 1-0.
The Australian denied Wayne Routledge, Chico Flores, Ashley Williams and Pablo Hernandez; with his fingertip save from the latter's curling effort the pick of the bunch.
The 40-year-old's contract is due to expire this summer, and he has already rejected the offer of a new deal
But Jol is remaining positive.
He said: "We offered him a new contract, the only thing is he wanted to be guaranteed to be the number one.
"That is not easy as we need a goalkeeper anyway. We don't know what will happen to (David) Stockdale and he does not want to be the number two, as you know he wants to be number one as well, and that is the problem.
"Okay, you can go on the market and find a useless goalkeeper, but you want a good goalkeeper and if you find a good goalkeeper you have to fight for your place, but we will sit down with him and try to find a solution.
"You saw today [Sunday], 3-0 looks very good but it would have been different if he had not been there."
He added: "We hope to find a solution, if we cannot find a solution we need to get a very, very, good goalkeeper because you need to be very, very good to be better than, or the same, as him."
Fulham's difficult conclusion to the season had led to suggestions Jol could leave his post at Craven Cottage.
But the Dutchman insists he will be in charge next season, and expects a busy transfer window with a host of loan signings returning to their parent clubs and other players out of contract.
"I am ambitious like Fulham are, I want us to be in the top six, the top seven or the top eight," he said.
"When I came here we had a fantastic team and we got 52 points, and look at where Swansea are today [Sunday] with 46.
"We do not want to repeat this season, only getting around 40 points, but we need good players, ambitious players and that is what I want."
He added: "If eight or nine players leave us this summer we will need five or six players."
Swansea manager Michael Laudrup, meanwhile, was left to rue a disappointing end to his first season in charge.
The Dane has guided the Welsh club to Capital One Cup glory and a ninth-place Premier League finish, but could not give the home faithful a fitting finale.
He said: "It was disappointing, but the difference was us not taking our chances.
"For 30 minutes in the second half we could have scored two or three.
"But I am sure in a couple of days I will see the big picture.
"Everyone here says it is the best season ever for this club. I have only been here 10 or 11 months so I will I trust their judgement."