Everton suffered a 5-1 loss against Arsenal at the Emirates Stadium on Saturday in the Premier League.
The Toffees poor run against Arsenal continued, the Merseyside based outfit have not beat the Gunners away since 1996.
Sam Allardyce made a surprise call to keep Oumar Niasse as his starting striker.
Niasse also got the nod mid-week in the 2-1 win over Leicester City but failed to take a shot on target.
Tosun was in for more bad news after the game as Big Sam said that he was struggling to adapt to Premier League football and that he may not become a regular starter until the end of the season.
Niasse was linked with an exit from Goodison Park over the winter transfer window but could now end up find himself as the Toffees first-choice striker.
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“So his service hasn’t been too bad but his hold up play hasn’t been like it was at Besiktas so that’s why he’s not starting the games at the minute because he’s finding it tough going like every player does, particularly when they come in January,” Allardyce said in his post match press conference.
“I said we wanted goals, he scored goals in the Champions League and with Besiktas but may not hit the ground running for us. He hasn’t done that yet, I’m sure he will do eventually.
“I’m more concerned about the other players than I am about Cenk. I’m more likely to feed him slowly and give him a bit more time over the next few weeks and hopefully by the end of the season he starts games.”
Tosun joined Everton on the back of 14 goals and three assists for Besiktas in all competitions.
The 26-year-old was directly involved in six of the Black Eagles 11 goals in the Champions League, helping his former side finish the group stage as leaders.
The Turkey international has gone from preparing for a Last 16 clash against Bayern Munich to playing second fiddle to the Senegal international.
Niasse has only scored twice as a starter for Everton since joining the club in January 2016.