Forster again saved Celtic as he denied Siem de Jong's header from inside the box.
Virgil van Dijk then found James Forrest on the right wing with a sweeping 50-yard diagonal ball. The winger controlled the ball and put in a cross towards the near post, but no Celtic player could get on the end of it.
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Baram Kayal then blazed a shot over the bar after the ball fell to him outside the area.
The Bhoys continued their good spell of play and Kris Commons tried to chip the goalkeeper from distance, but saw his effort drift over.
Ajax pushed for a second and Viktor Fischer forced Forster to save shortly after coming on.
They came closer a few minutes later when Schone shot at Forster after being put through.
Denswil also hit the post as the game reached its conclusion.