The Eredivisie side started former Premier League stars Jordan Henderson and Bertrand Traore, as well as ex-Juventus ace Daniele Rugani and old Man Utd target Brian Brobbey, but could not find a way through their stubborn hosts.
Their shocking defeat saw Ajax fall to 16th in the League Phase, four points off the top eight, thus officially ending their hopes of securing automatic progression to the round of 16.
AJAX endured a humbling 1-0 defeat to Latvian side RFS in the Europa League last night.
The Dutch side's opponents had not played a competitive match since the last round of European fixtures on December 12.
Per Global Football Rankings, the Latvian top flight is the 71st best football league in the world.
