Manchester: David Silva and Yaya Toure's goals earned Manchester City a 2-0 win over Bayern Munich but it was not enough to prevent them from being eliminated from the Champions League on Wednesday. (Agencies)
English Premier League leaders City went into the match knowing the only way they could progress into the knockout phase was to beat Bayern, who had already finished top of Group A, and for Napoli to fail to beat Villarreal.
Silva opened the scoring shortly before half time at Eastlands and Toure scored a second just after the start of the second period.
But Napoli's 2-0 victory at Villarreal, who had held the Italians for an hour, means Roberto Mancini's team will now have to combine their push for the Premier League title with a place in the Europa League.
Ultimately, their defeats at Bayern and Napoli earlier in the group stage proved costly to their hopes of extending their first Champions League campaign.
City knew they would have to be patient, even against a Bayern team that showed seven changes from the side that beat Werder Bremen 4-1 in their previous match.
But they created their first decent opening when Samir Nasri crossed from the right and Sergio Aguero headed wide from close range.
The hosts were dominating possession but Bayern went close with a quick break.
A long ball forward was flicked on by Nils Petersen and Ivica Olic's drive at the near post was turned wide by goalkeeper Joe Hart.
From the ensuing corner, midfielder Luiz Gustavo lifted a shot over the bar.
City had the ball in the net when Silva's free-kick floated into the top corner but referee Stephane Lannoy ruled Joleon Lescott had barged Bayern goalkeeper Jorg Butt.
The Germans continued to look a threat on the break and David Alaba missed from close range after the hosts had failed to deal with Anatoliy Tymoshchuk's cross.
Nasri also clipped a shot wide from the edge of the area after he stole the ball from Gustavo in midfield.
But after 36 minutes, City went ahead with a goal of real quality.
Silva had just been fouled by Gustavo but seconds after coming back on to the field, Edin Dzeko flicked Gareth Barry's pass to the Spaniard and he drove a shot into the corner of Butt's goal.
City continued to press after their breakthrough and after a wandering run, Aguero was only denied by former City defender Jerome Boateng on the line.
The hosts were getting the ball to Silva at every opportunity and the winger had a stinging shot pushed away by Butt before Barry prodded the rebound over.
City had a scare just after the restart when Danijel Pranjic burst forward from midfield and just missed the corner of the net from 20 yards.
But they doubled their advantage with a goal even better than their first.
Toure picked the ball up off Barry and, after feeding Aguero, the Ivorian surged forward to collect a pass from Dzeko to prod past the onrushing Butt.
The former Barcelona midfielder had scored just once in 33 Champions League matches before this season but his goal against Bayern was his third in six games in the competition this season.
Hart had to be alert to deny Alaba but Dzeko came close to adding a third with low drive from 30 yards.
And Barry had a drive turned away by Butt as the news filtered through that Napoli had taken the lead at Villarreal.
Nasri missed from 25 yards but City knew Napoli's lead in Spain meant their victory was in vain.
Manchester: David Silva and Yaya Toure's goals earned Manchester City a 2-0 win over Bayern Munich but it was not enough to prevent them from being eliminated from the Champions League on Wednesday.