Perhaps the arrival of Bayern Munich at Eastlands on Wednesday will be a blessing in disguise. A second league defeat of the season that was careless and avoidable left Manuel Pellegrini stunned and Manchester City's players with faces like thunder as they marched on to the team bus for the journey home, but bigger games have provided bigger performances so far this year.

Credit must go to Aston Villa for overcoming a 2-1 deficit with two goals in three minutes without their key players Christian Benteke and Gabriel Agbonlahor, but this game was City's for the taking after their dominant first-half display and having taken the lead twice.

Lackadaisical defending will have alarmed Pellegrini despite Karim El Ahmadi's initial equaliser appearing marginally offside, after Yaya Touré had put City in front. Joe Hart did not even make an attempt to save Leandro Bacuna's fine free-kick, which again reined City in after Edin Dzeko had restored their advantage from a corner, and the winning goal was Sunday league fare.

A long ball forward from Brad Guzan was flicked on by Libor Kozak and Andreas Weimann waltzed past the centre-halves and rounded Hart to finish into an empty net. Vincent Kompany and Matija Nastasic, woefully disorganised during that period, will need to be more alert when Pep Guardiola and co roll into Manchester this week.

"I don't think this result will have an impact [against Bayern]," said Pellegrini. "We know it is a different competition, we know that we must turn the page and think about the Champions League. I repeat I think that the team played a good match today but we have to revise a lot of things.

"For me the most important things are the three goals that Aston Villa scored. Especially the first and third goal, the second goal was a good free-kick. We will have to defend better, not only on Wednesday."

It was City's display at the back that was particularly alarming. Not only was this their second defeat of the campaign, but another example of a poor result away from home, where they have managed only one point from a possible nine. A defeat by Cardiff City and a draw at Stoke leave Pellegrini's side five points behind the leaders, Arsenal.

This was a shadow of the team that dismantled Manchester United so ruthlessly. City enjoyed 67% of the possession but against Paul Lambert's 3-5-2 formation, with Bacuna and Antonio Luna operating as wing-backs, all they had to show for their first-half dominance was a scrappy goal from Touré that wriggled through Guzan.

Once Villa found their rhythm and the Holte End its voice, City were overrun in the space of a frantic few minutes. Four shots on target and three goals – Arjen Robben, Thomas Müller, Franck Ribéry and Mario Mandzukic will be licking their lips.

Bayern have conceded two goals and scored 14 in their seven Bundesliga matches this season. City have not won a Champions League match at home since they overcame the German side in December 2011. However, having performed well in the Manchester derby and secured victory in their opening Champions League fixture this term, perhaps their strength under Pellegrini is on the big occasion.

City's manager, asked if his side were more motivated against stronger opposition, said: "If you only analyse the results of course, but I don't think it is about how the team thinks or feels. We tried to play exactly the same against the biggest teams or any other team.

"I think this match was very different than the ones we played against Cardiff or Hull. Today I saw the team playing the way we need to play and the way I want to play. Of course, this is not a good moment but they are professionals and we know how to raise our head again. We will try to win on Wednesday."

For Lambert, whose side have recorded victories over Arsenal, Norwich and now Manchester City this season, it was a first home win of the league campaign and, significantly, a result secured without their top scorer Benteke.

"I think too much has been made of the Christian thing," Lambert said. "I think Christian would be the first to say that we create the chances. For all the headlines he gets, he would be the first to say you need your team-mates. That's why it's hard to single out any player today because, as a team, they were brilliant."

Pellegrini will need his players to perform with equivalent unity when the European champions arrive in town on Wednesday evening.

Man of the match Leandro Bacuna (Aston Villa)