Manager Roberto Mancini, who failed to steer City out of the group stages in their debut Champions League season a year ago, took full blame for the defeat as he "didn't prepare well" for his Dutch opponents.
The loss left City with one point out of a possible nine and bottom of Group D, the only one of the competition's eight pools which features four national champions from last season.
Germany's Borussia Dortmund top the standings on seven points at the halfway stage, followed by Spanish champions Real Madrid with six, Ajax on three and City propping up the table following a draw and two defeats.
Despite Mancini's apology, the headline writers and reporters ripped into the Italian and his team with The Guardian writing: "If Group D is this season's Group of Death then Manchester City have just moved ominously close to having their toes tagged for the morgue."
The Times proclaimed: "City's limitations exposed again in Dutch masterclass" with the report dismissing their performance as "typical City".
The Telegraph said: "City head for early exit after Ajax ambush" adding, "Amsterdam is a suitable place for a watery grave and Manchester City's Champions League hopes were all but buried last night."
The collective transfer market worth of City's players on the field and the bench is approximately 300 million pounds ($480.88 million) - more than Ajax's entire playing squad.
But the Dutch champions taught their expensively assembled opponents a lesson in application, passing and team work as Ajax, champions of Europe four times, showed that it takes more than just money to turn a club into European aristocrats.
Mancini said his team now needed a "miracle" to reach the last 16.
"They were better than us. They played better football. It is my fault, I didn't prepare well for the game and I take the blame," the Italian said.
"I thought in one way and it was different. When you prepare in one way and it is a different game it is difficult.
"We had more chances to score and in the Champions League you need to score. It is my fault, I repeat. We change for five minutes to three at the back, but we always have 11 players.
"I don't think that is important. Three, four, five, six or seven defenders. If someone wants that as an excuse than ok, but it's not the reason. It is very difficult to qualify now. It would be a miracle."
Defender Micah Richards appeared to question Mancini's tactics, telling Sky Sports: "Three at the back is something that we have not worked on a lot. It is a hard system because we are not used to it, I think the players prefer a 4-4-2 but he is the manager and we'll do what he says."
Ajax manager Frank de Boer said his side's equaliser late in the first half had come at a crucial moment.
"That changed a lot for us," De Boer said. "Now we could underline the things that went wrong in the first half and go for a win in the second half.
Ajax's victory was the team's first at home against an English opponent in 32 years, the last coming against Nottingham Forest in 1980.