City now has just one point in its three Champions League matches and it was passed by Ajax in Group D, as Ajax picked up its first three points.
It is now going to take a remarkable turnaround and a little luck for City to do anything but get bounced early from this Champions League.
City's midfield struggled to get the ball in for good looks, and it was ineffective when Ajax had possession, and this led to City losing all control as this match wore on.
Samir Nasri got City off to a fine start and quieted the Amsterdam crowd with a nice shot in the far corner off a pass from James Milner in the 22nd minute for a 1-0 lead.
However, Ajax began to assert its will after that point, and in the 45th minute, Ricardo van Rhijn was given far too much space on the wing and he easily hit a low cross to Siem de Jong, who made a nice move and drilled the low corner for the equalizer.
It was all Ajax in the second half.
Christian Eriksen hit a wonderful corner in the 57th minute that was headed in by Niklas Moisander and Ajax fully seized control with a 2-1 lead. Then, Eriksen added his own goal by running circles around the City defense and ended up sliding in a deflected goal for a commanding 3-1 lead, as Ajax cruised to the finish.
Christian Eriksen: A
Christian Eriksen put his full potential on display in this match. The 20-year-old midfielder played outstanding, and he got better as this match went on.
He had some key passes and his brilliant play to score Ajax's third goal destroyed the will of Manchester City.
Eriksen is putting his name on the top of wish lists of plenty of clubs right now.
Kenneth Vermeer: A
Manchester City's weak attacks were consistently thwarted by Kenneth Vermeer, and for my money, the 26-year-old was the man of the match.
He made some excellent saves, and with each one, you could almost see City's confidence leaving. In the end, City wound up taking 16 shots, with five of them on target, and Vermeer turned all but one away.
Siem De Jong: B
Siem De Jong was not overly active and he spent stretches being a non-factor, but his goal in the 45th minute was the match's biggest play.
It changed the entire atmosphere of this match just as the teams entered halftime and it set the table for Ajax's big second half.
Joe Hart: C
Joe Hart wasn't done any favors by his defense. Ajax had far too many good looks, and the one goal where the defense did manage to get in position, the ball was deflected, making a save by Hart impossible.
Still, the goalkeeper allowed three goals off just six on-target shots.
Samir Nasri: B-
Nasri's quality goal in the early going should have set his team up for a needed win, and an A grade for Nasri. However, City just disappeared after that and Nasri went with it.
Nasri kept his effort high, but he was rendered completely ineffective as this match wore on.