Roberto Mancini's men needed a win to stand any chance of going into the final round of Group D fixtures with a qualifying place to play for, but fell behind to Karim Benzema's 10th-minute strike.
City rallied to equalise in the 73rd minute when Aguero slotted home from the spot after Alvaro Arbeloa's foul on the striker earned him a red card, but City could not make its numerical advantage pay and slid out of the competition.
Meanwhile Borussia Dortmund guaranteed progression as Group D winner with Robert Lewandowski scoring twice in a 4-1 thrashing of Ajax at the Amsterdam ArenA.
Marco Reus, Mario Gotze and Lewandowski put the in-form German side out of sight by half-time, and after Lewandowski had added his second of the night, Danny Hoesen grabbed a consolation for the home side with four minutes left.
