Nasri handed City the lead after a slow start at the Amsterdam Arena, but goals from De Jong, Moisander and a deflected Eriksen effort have left their European hopes in tatters
The visitors took their time to grow into the tie but made no mistake with their first opportunity - Samir Nasri slotting home. However, Siem de Jong netted a superb equaliser on the stroke of half-time to send Roberto Mancini's men into the break with a bitter taste in their mouths.
After a cautious start to the second 45, the Dutch side took the lead through Niklas Moisander before Christian Eriksen inflicted further pain with a deflected shot to bag the third, condemning City to a disappointing blow.
The result gives the Dutch giants their first victory in this year's group stage, while City have just one point from three matches and face a mountain to climb to escape this season's 'Group of Death'.
Danish playmaker Eriksen starred for the Dutch champions, with former Liverpool man Ryan Babel also among the recognised names in the starting XI.
Eden Dzeko was handed a start after his last minute winner against West Brom at the weekend, with Sergio Aguero partnering him in attack. Elsewhere, James Milner kept his place in the side despite being sent off against the Baggies.
The hosts made the brighter start, keeping the ball with ease and working the first chance of the game just before the ten minute mark, but Eriksen fired narrowly wide of Joe Hart's post.
The dangerous Eriksen then flattened Yaya Toure with a hefty challenge, leaving the Ivorian down but not out, before the Dane made his mark in a different way, once more going close with a long-range effort after producing a delightful touch to set himself up.
However, somewhat against the run of play, Mancini's men took the lead in the 23rd minute. Micah Richards fed Milner with a beautifully weighted ball, with the midfielder passing it on to Nasri who opened his body to curl a shot past Kenneth Vermeer.
Aguero then twice found himself with space in the box, and may well have doubled the lead if it wasn't for two last ditch tackles, before, five minutes later, Vermeer made a fine save from Richards as the Premier League champions settled.
With half-time approaching City were made to pay for failing to press on, though. Ricardo van Rhijn delivered with a low cross from the right, picking out De Jong's run and allowing the midfielder to smash a first-time effort into the corner, giving Hart absolutely no chance and sending the teams into the break on level terms.
The visitors almost made the perfect start to the second period. Aguero broke into the Ajax box and, as Vermeer rushed out, tried to find a team-mate in the area but saw his chipped cross cleared.
However, after a quiet 15 minutes or so, the exact opposite happened. Eriksen whipped in a fantastic corner from the right-hand side, with Moisander then beating Joleon Lescott in the air to nod it past a helpless Hart.
Things went from bad to worse for Mancini, minutes after replacing Lescott with Aleksandar Kolarov and switching to a back three. The Dutch outfit's man of the match, Eriksen, embarked on a twisting run before unleashing a left-footed effort, the ball striking Gael Clichy on it's way into the goal - once again giving Hart no chance.
Tobia Sana then had a golden chance to put his side further ahead, Hart rushing off his line very quickly to smother the one-on-one. Then, as City rushed forward, Dzeko squandered two opportunities to give the visitors a lifeline - the Bosnian hesitating slightly on both occasions which allowed Vermeer to make the blocks.
For the final 15 minutes or so Mancini's side seemed to be playing with just two men at the back and two in midfield, with Mario Balotelli and Carlos Tevez both thrown into the fray.
Nasri had a weak penalty appeal turned down and Aguero shot narrowly over, but ultimately there was no breakthrough and Ajax held firm to secure their first win of the tournament, leaving City in big trouble.