The prize of eighth place to go along with their League Cup win against Bradford City in February was up for grabs for Swansea but they struggled against a disciplined Fulham.
Bryan Ruiz was the first to threaten when escaping the offside trap but he wanted too much time on the ball and eventually fluffed his shot wide.
Swansea then enjoyed a spell of possession around the Fulham 18-yard box but other than a Pablo Hernandez strike that flashed just wide from 22 yards they never really looked like scoring.
Then the breakthrough came. Emmanuel Frimpong did well in midfield and Ruiz's back flick return gave him time to pick Alexander Kacaniklic out and he finished well past Michel Vorm on 22 minutes.
Kacaniklic then had the game's next opportunity. Fulham were awarded a free-kick and, while Swansea were sleeping, Vorm needed to be at his best as he tipped onto the post from the Swede.
As the game approached the interval Jonathan de Guzman headed wide from Angel Rangel's cross when it appeared Michu had a far easier chance just behind him.
At the start of the second half, Michael Laudrup's men certainly had a go and could have equalised at least three times.
Hernandez set Wayne Routledge in when he could have shot but the winger's attempt hit the side-netting.
Hernandez was then played in by Rangel but Mark Schwarzer was equal to it and made the save. Moments later De Guzman picked out Ashley Williams but the ball hit him and then the post, and it looked like it was going to be Fulham's day.
Then, on 77 minutes, Dimitar Berbatov sneaked through by rounding Vorm before passing into the empty net after the Bulgarian's lovely run was picked out by Ruiz.
Swansea did not let that deflate them too much but they appeared to run out of ideas and, for the first time this season, the home fans started to show their frustrations.
In stoppage-time Swansea's misery was complete as substitute Urby Emanuelson tapped in after Kacaniklic's shot was saved.