Manchester City are staring at the possibility of leaving the Champions League, just as they were beginning to get acquainted with the competition. They picked a bad time here to misplace the form that has accompanied their rise to the Premier League's summit and are left with the considerable task of having to beat Bayern Munich, the four-times winners, to stand any chance of qualifying.

Even then, it may not be enough. Whatever happens at the Etihad Stadium on 7 December, Roberto Mancini's team will be condemned to the Europa League if Napoli go to Villarreal and win. City may hope for a favour in the final round of Group A fixtures given that Bayern are already through but, equally, the Germans seldom take these assignments lightly, particularly if it means eliminating the team currently at the top of English football. The more pertinent fact may be that Villarreal, without a point, have nothing to play for. "I hope they play a serious match," Mancini volunteered afterwards.

It represents a difficult position, to say the least, for a club with City's ambitions and, for that, they will reflect on a hugely disappointing night. They were beaten by Edinson Cavani's two goals, the Uruguayan opening the scoring in the 17th minute and then re-establishing the lead early in the second half. Mario Balotelli equalised in the 33rd minute but there were only flashes of City's best form and, despite a late onslaught on the home goal, they failed to cope adequately enough with the challenges that were set in this whistling, firecracking, bearpit of a stadium. City's only victories in the Champions League have come against Villarreal and, though Mancini argued he was "not disappointed" with the performance, there is no question they have come up short throughout the competition, going behind in four of their five matches.

The first lesson is about the importance of asserting control. City began the game encouragingly, knocking the ball around nicely and playing with the calmness that might be associated with a team that have accumulated 42 goals in their first dozen league fixtures. But then they became careless and unusually dishevelled, a spell culminating in the kind of soft goal that will make Mancini wince when he sees the replays.

By this point Marek Hamsik had already headed a presentable chance into Joe Hart's arms and Ezequiel Lavezzi had shot narrowly wide after a lovely exchange with Cavani. Hart then tipped Gokhan Inler's long-range shot over the crossbar and it was from Lavezzi's corner that Napoli scored. Cavani flicked the ball goalwards at the near post and the closest defender, Aleksandar Kolarov, was unable to clear before it ricocheted off Hart's knee into the net.

As the volume went up, City needed time to regain their composure and they were grateful that Napoli would be just as obliging with their defending for Balotelli's equaliser. David Silva, increasingly prominent towards the end of the first half, was presented with the ball inside the penalty area and the Spaniard reacted to Salvatore Aronica's loose clearance with a quickly taken shot that the goalkeeper, Morgan De Sanctis, could only parry. Balotelli, playing despite a fever and later seen vomiting on the pitch, turned the ball into an exposed net.

Suddenly the decibel level went down a few notches and, with the interval approaching, City became as the more composed team. Silva was at the hub of it and when he played in the overlapping Kolarov just before half-time De Sanctis could not hold the shot again. This time, however, there was no one in a City shirt to get to the rebound.

Yet what has sometimes been overlooked during City's free-scoring start to the season is that they have not been defending with the parsimony of last season. Four minutes into the second half, Napoli put together a wonderful exchange of penetrative passing, culminating in Andrea Dossena picking out Cavani inside the penalty area. The Uruguayan's first-time shot was struck expertly, combining power and precision in equal measure.

Two-one down, City had to commit more men forward, making for a compelling final half hour. Mancini was entitled to reflect on his team's late pressure – "We didn't deserve to lose," he said – but they were also vulnerable to the counterattack. Lavezzi broke clear only to be denied by Hart and, shortly afterwards, Hamsik tricked Kolarov, advanced into the penalty area and flashed a shot against the post.

Then Balotelli had a couple of chances to salvage the draw that would keep City second in their group. The first was saved. The second was headed over the crossbar. The final whistle blew and City were left to contemplate whether their first season in the Champions League might be nearing its end.