“The players are to blame for the recent results, we will make Slaven Bilic proud of us and everybody will applaud him and appreciate what he has done for this club,” Uysal was quoted as saying by the Hürriyet.
Beşiktaş are currently managed by Bilic but he the Croatian head coach is expected to leave at the end of the season.
The Black Eagles crashed out of the title race on Monday 18 May after losing 1-0 against Konyaspor at the Osmanlı stadium in Ankara.
The Istanbul giants take on Galatasaray next in the derby and can still finish as runners up if they win their next two games and if Fenerbahçe drop points over the next fortnight.
Bilic has yet to record a derby victory against Fenerbahçe or Galatasaray since joining Beşiktaş in 2013.
Bilic is expected to part ways with Beşiktaş and join West Ham at the end of the season.