City are out of the Champions League following a 3-1 defeat to Monaco.
Leroy Sane looked to have saved the day with a late goal that briefly put the Blues back in front on aggregate, but the hosts rallied to score a third five minutes later to tie the overall score at 6-6 - enough to progress to the last eight on the away goals rule.
It is a crushing blow for a team that had previously gone 11 games without a loss, but the price of a poor first-half display when City were, at times, overrun by the rampant Ligue 1 leaders.