Roberto Manciniâ€™s men required maximum points and needed Villarreal to avoid defeat at home to Napoli and although they held up their end of the bargain, the Spaniards didnâ€™t as they lost 2-0 to the Italians.
Bayern were without Arjen Robben altogether and the likes of Franck Ribery, Mario Gomez, Manuel Neuer, Philipp Lahm and Thomas Mueller were all on the bench indicating that manager Jupp Heynckes was settled on his sideâ€™s top position and had no intention of winning this one.
Man City were working towards an opener and it came in the 36th minute when David Silva controlled an Edin Dzeko flick-on with his chest outside the area before hitting the bouncing ball unerringly into the bottom corner past Hans-Jorg Butt for a vital lead.
City looked far more likely to score again and their second goal came seven minutes into the second half when Yaya Toure, who started the move, ran onto a clever ball from Dzeko to slot home just before an advancing Butt making it 2-0 and sending the Etihad Stadium fans in raptures.
The home side had plenty of other chances, namely Sergio Agueroâ€™s early missed header, ex-City defender Jerome Boatengâ€™s sliding save to deny Aguero in the 39th minute and a number of strong save from Bayern keeper Hans-Jorg Butt.
Although City got the required result, things did not fall their way in the end and they will now have to drop down to Europeâ€™s second tier club competition where they will join neighbours Manchester United who lost 2-0 at FC Basel to miss out on the knockout phase.
Champions League Group A
Yellow cards: MANC - nil
BAYM - Ivica Olic 14â€™, Luiz Gustavo 35â€™