The defeat against the Anatolian Eagles ended the Istanbul giants title hopes and put securing a Champions League place in jeopardy.
“I do not expect Beşiktaş to keep me on at the end of the season,” Bilic said speaking on Lig Tv after the game.
Bilic has been closely linked with a move to West Ham over the past few weeks but denied being in talks with Hammers.
The Daily Star recently reported that Bilic is prepared to hold talks with West Ham to replace Sam Allardyce this summer.
Former West Ham player Alvin Martin has made Bilic his favourite to take over in the summer.
“I wouldn’t rule Slaven out. He’s been round the game for a while now. He’s proved he could do it at international level and club level in difficult circumstances,” Martin said speaking on the Alan Brazil Sports Breakfast show on TalkSport.
“I know him. He’s a highly intelligent and highly motivated individual. I think he would be absolutely perfect for us [West Ham].
“Slaven is the outstanding candidate for me.”
Beşiktaş are currently third in the Süper Lig, seven points behind league leaders Galatasaray with two games remaining.