The home side took the lead midway through the first half after a neat finish from 18-year-old Wesley Jobello.
Work in progress: Roberto Mancini's young stars have some making up to do
City responded well after the break but Marseille weathered the onslaught and grabbed two goals on the counter attack through Najib Ammari and Florian Moulet in the dying minutes.
Man City, who are yet to register a victory in the competition, next face Scottish champions Celtic while Marseille are three points behind group leaders Barcelona.
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