Sergio Aguero put City level 15 minutes from time, but they could not force the winner as they suffered yet more disappointment in Europe.
Here, Sports Mole dissects the 90 minutes of action between the two Group D rivals.
On target 6
On target 5
Was the result fair?
On the balance of play, you would have to say yes. Ajax were the better side on the ball this evening, but City did have a host of chances in the latter stages of the match. Neither side deserved to suffer defeat, but City will feel aggrieved that they were not awarded a penalty in the final moments. The fact of the matter is, however, City have not turned up in the Champions League this season.
Manchester City's performance
4/10. City would have won this match last season. It is as simple as that. There is just no tempo to their play at the moment and they do not look entirely comfortable in forward positions. Toure scored a fine opener for his side, but he disappeared after that and even Vincent Kompany did not look entirely happy.
7/10. Make no mistake about it, this Ajax team can play. In many ways they are a typical European outfit, very good on the ball, but susceptible when under constant pressure. As it stands they are in the mix for qualification, but are also in the driving seat to secure third spot and a place in the Europa League.
Sports Mole's man of the match
Siem de Jong: The 23-year-old striker occupied a deeper role this evening and was just magnificent for Ajax. He already has eight goals this season and his touch and awareness on the ball was sublime. Ajax will do very well to keep hold of the Dutchman beyond January. He is that good.
Biggest gaffe of the match
City's defending for the opening two goals was dreadful. Zonal marking has been spoken about in length this season and they were caught by two soft corners in the opening 17 minutes.
Peter Rasmussen had a fairly eventful 90 minutes of action. He might have awarded City a penalty inside the opening five minutes and perhaps should have blown for a spot kick in the final seconds, but he signalled the end of play instead.
Manchester City: City will attempt to continue their unbeaten start to the Premier League when they host Tottenham Hotspur on Sunday, before facing a must-win home game against Real Madrid in the Champions League on November 21.
Ajax: The Dutch outfit will return to league action against PEC Zwolle on Sunday. Meanwhile, their next Champions League clash is at home to Borussia Dortmund on November 21.