French center back Mapou Yanga-Mbiwa decided the match with a header following a free kick in the 85th minute his first goal of the season.
Nasri will be out for eight weeks after partially rupturing ligaments in his knee in the second half of City's 2-0 win.
Yanga Mbiwa, 23, has won three caps and is regarded as one of the top centre backs in France.
Blanc decided to travel to Ukraine with seven defenders and no recognised playmaker.
France coach Laurent Blanc included uncapped defender Mapou Yanga-Mbiwa and out-of-form midfielders Yoann Gourcuff and Alou Diarra in a 26-man provisional squad.
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