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, 3-0 looks very good but it would have been different if he had not been there."