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. A side cannot hope to make an impact on the Champions League with this form of carelessness and perhaps most dispiritingly for a club of their ambitions, they are threatening to go out of the competition with a certain amount of ignominy attached.

Three games in, this defeat leaves the Premier League champions with only a solitary point and hard evidence about their inability to adapt to Europe's elite club competition. Samir Nasri's goal offered hope 22 minutes into the first half but the capitulation that followed merely affirmed the sense that City, and Roberto Mancini, have not yet fully grasped what is required in Europe.

They have seldom looked so vulnerable in the Mancini era and from where they now find themselves, it is going to need an extraordinary feat of escapology. As it stands, City are bottom of their group and might not even be playing in the Europa League come February.

Ten points was not enough for them to qualify last season and this group does not get any easier. City's next assignment is also against Frank de Boer's Ajax team, followed by a home game versus Real Madrid and the problems they invariably pose, and then a trip to Germany to face the Borussia Dortmund side who made Mancini's men look so ordinary at the Etihad Stadium three weeks ago.

If they are still in contention when they reach the Westfalenstadion it should probably be seen as a victory of sorts. Mancini talked of needing "a miracle".

This section was always going to be difficult, incorporating the Dutch, Spanish and German champions, but the fact is City have been guilty too often of making life unnecessarily hard for themselves. Siem de Jong's equaliser was a soft goal to concede but Ajax's second, coming from a corner, probably best epitomised the deterioration in their defending this season. The third was fortuitous, Christian Eriksen's shot taking a sizeable deflection off Gaël Clichy, but the defending before that moment was poor again.

As for Mancini's tactics, the Italian should not be immune from criticism because of what he has achieved in other competitions, and it was difficult to fathom his thinking. Mancini began with Sergio Agüero on the left wing then abandoned his 4-2-3-1 system early in the first half, tried out 4-4-2 and then ditched that for 3-5-2. With so many changes, it was not entirely surprising the team looked so dishevelled. Micah Richards's comments afterwards about the players preferring a flat back four hardly dispelled the lingering accusation that Mancini's managerial qualities have been seen only fleetingly in this competition over the years.

More than anything, this was a night when City seemed to have misplaced everything that brought them success in the previous couple of seasons.

They looked hesitant, lacking leadership. Their play was pockmarked with individual mistakes and it was only at 3-1, when the situation was desperate, that they began to attack with any real penetration. The best chance, however, fell to Ajax's Tobias Sana, clean through but denied by Joe Hart's goalkeeping.

Even the opening goal was largely against the run of play, stemming from their first noteworthy attack. Nasri finished off James Milner's pass confidently, running in from the left and applying just the right amount of curl to bend his shot into the opposite corner.

Briefly it unsettled Ajax and discontent could be heard in the home stands. Yet the game lurched back in their favour in first-half stoppage time when Ricardo van Rhijn, one of seven academy graduates in the Ajax side and hugely impressive, put in a low centre and De Jong lashed a first-time shot past Hart.

Gareth Barry's part in that goal was pretty undistinguished, with only a half-hearted attempt to intercept the cross, and the same player was partly to blame in the 68th minute for Ajax's third, losing the ball to Lasse Schone in the build-up to Eriksen's deflected left-foot shot.

In between, Niklas Moisander's goal to make it 2-1 was even more harrowing from a City viewpoint. Eriksen swung in the corner from the right and Moisander out-jumped Joleon Lescott to divert the ball inside an unguarded far post.

It was standard stuff, but this was a substandard night for City – one with considerable repercussions, potentially, unless they achieve the miracle their manager talked about.