City's US tour is over after Olympiacos became the second team in four days to beat Manuel Pellegrini's men on penalties.
Most of the talk pre-match had been about the state of the TCF Bank Stadium pitch, but it was deemed playable after an early morning inspection and in front of more than 34,000 fans, the game went ahead in temperatures approaching 90 degrees.
City drew first blood when Stevan Jovetic continued his rich vein of form with the opening goal on 35 minutes as he collected the ball, drifted past two challenges before selling a dummy and poking the ball home.
Olympiacos drew level within two minutes through the lively Dimitrios Diamantakos who finished coolly after a defensive mix-up by the Blues.
City started the second-half well and regained the lead on 51 minutes when David Silva was fouled in the box and Aleks Kolarov made no mistake from the spot.
There were chances to increase the lead before Diamantakos scored his second of the game with 66 minutes played and though both teams went close before the end of normal time, a penalty shoot-out once again was needed to decide the outcome
The Blues started this one better with Silva and Kolarov both converting their kicks and Hart saving one of the Olympiacos attempts. But with the advantage, Milner and Sinclair then missed leaving Hart to save the Greek's fifth penalty and ensure sudden death.
Unfortunately, Micah Richards hit his well over the bar and Papazoglou made no mistake to clinch the game 5-4 for Olympiacos.