Fellow ex-Man United manager Ole Gunnar Solskjaer and his Besiktas side earned the win thanks to a 44th minute Gedson Fernandes strike.
Defeat to Besiktas leaves Fenerbahce eight points behind league leaders and arch-rivals Galatasaray with four games remaining.
Mourinho, 62, has had several clashes with referees in Turkey, forcing the Turkish FA to appoint Slovenian referees for their games.
Speaking to the press after the game, Mourinho believes the title winner was predetermined and his side never stood a chance.
He said: "When some of your players don't perform well enough, it affects your collective performance as well.
“The outcome of the league was determined before the league even started. The games we lost at home were decisive. VAR decisions, referee decisions.
“I am so tired of talking about these. I have no power, nothing changes, but this is the situation, this is the truth."