The Cottagers have lost six of their last seven league games and currently lie in 15th in the table, though a win on Sunday could see them finish as high as 10th depending on other results.
And Jol believes a win would do much to dampen growing criticism of him and his players, and is determined to give the Cottagers' travelling support something to cheer about.
"I would love to have a good result over there," Jol told reporters. "That would put everything in perspective again if we could finish this season off on 43 points.
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"It will be a boost for us if we can win and for the 800 or 900 fans we take with us."
With Swansea currently six points ahead of Jol's side, the Dutchman cited the two teams' previous meeting earlier in the season - ending 2-1 to the Welsh side - as evidence of how slim the margin are in the Premier League.
"The difference between us and Swansea is the game at Craven Cottage. They've got 46 points, we've got 40," Jol added.
"We were the first team that had more possession against them, but two goals due to our defence gave them the win.
"If we had won, we would have both been on 43 points but they [according to pundits] were fantastic and we were useless this season. That is the Premier League, it is a thin line."
Jol believes his side's frailties this season were largely caused by the influx of loan signings, which have masked Fulham's lack of squad depth this season.
"Last year we had a big problem and we managed to get these players in on loan and everyone was happy," he recalled.
"Later, it probably turned a bit against us because we had too many players on loan and we knew that. It is not a healthy situation but that was the situation and we still managed to stay in the league and get 40 points.
"I can explain these indifferent results but, on the other hand, it is a result-related business."