The Eredivisie side had the bulk of possession and captain Davy Klaassen wasted a couple of chances to put the ball in the net, but instead they had to make do with a third draw from four Group A outings.
Their Turkish opponents, two points better off, could not have complained had they been beaten but saw Fernandao spurn the best chance of the game in the closing minutes.
The home side’s brightest spark early on was Anwar El Ghazi but he lasted little more than half-an-hour before coming off with an injury. His replacement Lasse Schone was equally bright but despite a majority of possession, there was little end product and, at the other end, Jairo Riedewald needed to be alert to deal with a dangerous corner just before the break.
Viktor Fischer was a second injury loss for Ajax but the game remained in their grasp.
Good work by Tete allowed Klaassen a sight of goal in the 56th minute but he shot wide.
The captain spurned a second, even better, chance when Riechedly Bazoer and Schone combined well only for Klaassen to blaze over.
Fener, so long on the back foot, might have stolen the points with eight minutes remaining.
Substitute Fernandao’s eyes lit up when the goal opened up in front of him but he somehow missed the target.
Volkan Demirel saved from Amin Younes in added time to ensure a stalemate.