Things could have been even worse for Roberto Mancini's men as they needed goals from Yaya Toure and Sergio Aguero to wipe out two early strikes from Ajax captain Siem de Jong, but their plight in Europe's premier competition is now even more precarious having failed to win any of their opening four group games.
City had made a promising, purposeful start to the game and, having seen an early penalty appeal turned down, could have hit the front when Samir Nasri threaded a clever pass into the box for Pablo Zabaleta, only for the Argentine full-back to blaze wastefully over.
Ajax took full advantage of the let-off with the opening goal just moments later; City's defenders allowed a corner from the right to drop and, after Niklas Moisander had prodded forward, de Jong slid in from an acute angle to lift a deft finish over the prone Joe Hart.
The visitors doubled the lead on 17 minutes as de Jong punished more slack City defending at a corner. Christian Eriksen swung in a delivery, this time from the left, and the Ajax skipper was allowed to drift unchallenged to the near post by Yaya Toure where he glanced home a simple, clinical header.
To their credit City responded quickly and reduced the deficit within five minutes. Moisander failed to deal with Nasri's cross and his unconvincing header dropped to Toure who, whilst fending off Ricardo van Rhijn, controlled on his chest before spinning and flashing an acrobatic volley past Kenneth Vermeer.
Van Rhijn was then forced to clear from underneath his own bar, although Gareth Barry's challenge on him was subsequently deemed illegal in any case, while Vermeer had to be alert to stop a Zabaleta header after another enterprising dart into the box had been picked out by Javi Garcia.
But, despite those scares, the visitors were decent value for their lead at the interval with the controlled midfield promptings of de Jong, Eriksen, Lasse Schone and in particular Christian Poulsen ensuring they remained the more cohesive, measured unit.
With victory imperative, Mancini went on the offensive as he brought on Mario Balotelli for Garcia at half time and, after a noticeably lifting the tempo, his side had the chance to draw level on 50 minutes as the unmarked Matija Nastasic volleyed over after being picked out by a Barry free-kick from the left.
Sergio Aguero did find the net with a smart finish only to see his effort correctly ruled out for off-side, but Ajax and de Jong served a potent reminder of their continued threat as the midfielder fired in a vicious long-range strike and then a curling free-kick that Hart had to be alert to push away.
But City's urgency paid off on 74 minutes with a simple equaliser; Hart's long clearance was flicked on by Balotelli and Aguero showed pace to get ahead of Toby Alderweireld and then typical composure to direct an angled finish into the corner from the edge of the box.
The Argentine thought he had won the contest in the dying moments only to see another effort ruled out for offside, although this time the call against Aleksandar Kolarov looked dubious, and the game ended in controversy as Balotelli saw what appeared a convincing penalty shout ignored by Danish referee Peter Rasmussen who instead chose to blow the final whistle.