The Barclays Premier League side now prop up the group after collecting just one point from three matches.
They had reaped the rewards of a positive start in Amsterdam. Samir Nasri provided City with a lead after just 22 minutes, Micah Richards bustled down the right wing, with James Milner then feeding a neat pass to the feet of the Frenchman to steer a shot into the net. Ajax had been viewed as the weakest team in the group and City seemed intent on proving it.
Edin Dzeko had been rewarded for a resurgence in form by starting alongside Sergio Aguero in the City attack and the pair combined well in the first half. One backheel from Dzeko set up his strike partner to shoot on goal.
Yet Ajax were not lying down in the face of such an expensive line-up. The Dutch side are not without their own esteemed talent and they equalised on the cusp of half-time when Gareth Barry failed to cut out a low cross and Siem de Jong planted a firm strike past Joe Hart.
The hosts maintained their urgency after the break and went ahead after 57 minutes. Niklas Moisander got in front of Joleon Lescott to glance a header into the net from a corner.
City were rattled and they were soon knocked to their knees. Nasri had flashed two efforts at goal but City would succumb to just one from Christian Eriksen. His darting run across the area worked space and his shot reared up off Gael Clichy and past Hart.