Switzerland won the 68th Eurovision Song Contest with the song "The Code" performed by Nemo.
Windows95man's "No Rules" ranked 19th out of the 25 competing entries in Saturday's final in Malmö, Sweden.
The lead-up to the pan-continental pop contest saw protests against Israel's participation because of the war in Gaza.
In the final, Israel rose to fifth place, with Finland giving Israel the maximum 12 points in the public vote.
Shortly before it was time to present Finland's jury points, Finnish artist Käärijä, who was the runner-up in last year's Eurovision Song Contest, said he wasn't going to announce the results.
"I have decided to step back from giving points in tonight's Eurovision. Distributing points in tonight's final does not feel right," he said.
The Finnish public votes were instead announced by an Yle radio host.
On Saturday, a group of protesters arrived at the Yle premises in Pasila, demanding Yle withdraw from the contest. This week some 1,500 musicians and industry professionals signed a letter calling on the Finnish public to avoid the show.
Windows95man had publicly stated their opposition to Israel's participation in the competition and considered withdrawing but ultimately decided to perform.
Second place in the contest went to early favourite Croatia, represented by Baby Lasagna with the song "Rim Tim Tagi Dim." Ukraine rose to third place, while France took fourth. Israel, represented by Eden Golan with the song "Hurricane," came in fifth.
Each participating country awards two sets of points to their favourite songs. One set is given by a professional jury, and the other is from viewers watching the show.
Windows95man attracted a total of 38 points, with the winner earning 591.
Watch Teemu Keisteri and Henri Piispasen perform their Windows95man act at the final:
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