The English champions were looking for their first win of the campaign, but despite taking the lead against the run of play through Samir Nasri, they fell to goals from Siem de Jong, Niklas Moisander and Christian Eriksen in Amsterdam.
The visitors finished the game with Edin Dzeko, Sergio Aguero, Carlos Tevez and Mario Balotelli all on the pitch, but by the full-time whistle they found themselves looking down the barrel of another autumn elimination.
Ajax move into third place after claiming a first home win over English opposition since 1980, leaving City bottom of the pool with a solitary point to their name after three games.
Matters were compounded by Borussia Dortmund's 2-1 win at home to Real Madrid in the other group game.
City now trail Dortmund by six points, Madrid by five points, and Ajax by two, and may need to win all three remaining games -- starting with the return fixture against Ajax on November 7 -- to stand any chance of going through.
"I think that they played better than us. They played better football," crestfallen City coach Roberto Mancini told Sky Sports.
"It's probably my fault because I didn't prepare the players well for this game. I accept fault for this defeat.
"When you prepare a game, you prepare it one way, you think it will be like this and sometimes, instead, it's different.
"I think it's very difficult now (for City to qualify)."
Dzeko had been rewarded for his brace at West Bromwich Albion on Saturday with a starting place in the City attack, but neither he nor strike partner Aguero were given much to work with in the first half.
Eriksen, Ajax's highly coveted Danish playmaker, helped the hosts pin City back, cracking a half-volley just off target in the ninth minute and then drilling wide from 20 yards after leaving Gareth Barry for dead.
It was one-way traffic, but City exploited their first real sight of goal in the 22nd minute to take the lead.
A gloriously incisive pass from Micah Richards found James Milner and he rolled the ball into the path of Nasri, who bent a first-time shot inside Kenneth Vermeer's left-hand post from 15 yards.
Vermeer then had to beat away a shot from Richards but Ajax were quickly back on the attack, with Ricardo van Rhijn to the fore.
The goal was recompense for Ajax's enterprise and in the 57th minute they procured another, Finnish centre-back Moisander rising above a static defence to meet Eriksen's right-wing corner with a glancing header.
Mancini responded by introducing Aleksandar Kolarov from the bench and switching to a three-man defence.
The Serbian teed up Milner for a header that went over the bar, but the defensive re-shuffle seemed to confuse City's defenders and moments later, the Dutch champions made it 3-1.
After Barry slipped in midfield, Eriksen took up possession and beat Vincent Kompany before dispatching a shot that took a cruel deflection off Gael Clichy to leave Joe Hart with no chance.
The England goalkeeper came out superbly to thwart Tobias Sana moments later, before the visitors roused themselves.
Vermeer saved twice, brilliantly, from Dzeko, but despite the introductions of Tevez and Balotelli, City were unable to conjure up the kind of improbable escape that had seemed to be becoming their trademark.
Manchester City face elimination after Ajax defeat
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