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Victory at Polish side Lech Poznan would have taken big-spending City into the next round, but despite dominating the early exchanges they fell behind in the 30th minute when Dimitrije Injac drove the ball home.
Emmanuel Adebayor, who scored a hat-trick in the reverse fixture two weeks ago, drew City level early in the second half when he lashed in the rebound after home goalkeeper Jasmin Buric saved his header.
There was a cruel sting in the tail for the visitors, however, as Lech restored their advantage four minutes from time.
The goal had a touch of the comical to it, with City centre-back Dedryck Boyata inadvertently heading the ball against Manuel Arboleda's head and the ball rebounding into the City net.
The Polish side made sure of victory in the first minute of injury time, with Mateusz Mozdzen crashing a sweet drive into the top-left corner from the edge of the box to condemn City to their third straight defeat.
"This is football," said City coach Roberto Mancini.
"Probably if we played this game another 100 times we would win 90 times, maybe. But we must accept this. We must continue to work because sometimes you lose games you don't deserve to lose."
Lech and City are level on seven points at the top of Group A, with Italian giants Juventus three points off the pace after a disappointing 0-0 draw at home to Red Bull Salzburg.
Liverpool once again had skipper Gerrard to thank for a rousing 3-1 comeback win over Napoli at Anfield.
Ezequiel Lavezzi had put the visitors in front after scampering in behind the Reds defence in the 28th minute, but Gerrard restored parity with 14 minutes remaining, latching onto a poor back-pass before slotting home.
He then stepped up to dispatch an 88th-minute penalty after Glen Johnson had been tripped in the penalty area, before completing his hat-trick a minute later by dinking the ball over Napoli goalkeeper Morgan de Sanctis.
The result enables Liverpool to go five points clear of the Italians, who drop to third behind Steaua Bucharest in Group K.
CSKA secured one of the two qualifying berths in Group F after coming from behind to beat Palermo 3-1 in the Russian capital and maintain their 100 percent record.
Massimo Maccarone put the visitors ahead in the 10th minute but Japanese international Keisuke Honda equalised shortly after half-time and a quick-fire brace by Tomas Necid took the Muscovites through.
Fellow Russian Premier League side Zenit Saint-Petersburg, the 2008 champions, also progressed, along with Stuttgart, Porto and Belarusian representatives BATE Borisov.
Paris Saint-Germain spurned the chance to progress as they registered a goalless draw at home to German league leaders Borussia Dortmund, which allowed Sevilla to claim the Group J lead by thrashing Karpaty Lviv 4-0.
Holders Atletico Madrid won 2-1 at Rosenborg thanks to an 84th-minute winner from Portuguese midfielder Tiago Mendes.
The side from the Spanish capital are a point behind Group B leaders Bayer Leverkusen after a goal in the 90th minute by Arturo Vidal gave the German side a 1-0 win over Greek outfit Aris.
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