Manchester City are out of the International Champions Cup following their second penalty shootout defeat in four days on their tour of the USA.
Olympiakos fought back to draw 2-2 in Minneapolis and then won the resulting shootout 5-4 as goalkeeper Roberto Jimenez Gago saved two penalties.
Following a similar defeat by Liverpool at Yankee Stadium, City head home.
After the match, City confirmed they had signed Frank Lampard, 36, on loan from New York City until January.
Striker Stevan Jovetic opened the scoring against Olympiakos after 35 minutes and, after Dimitrios Diamantakos equalised, Aleksandar Kolarov put the English champions 2-1 up from the penalty spot.
But 21-year-old striker Diamantakos’s second goal of the game levelled the scores on 66 minutes and the Greeks held on for the draw.
City had to win to have any hope of reaching the final on 4 August but paid the price for penalty misses by James Milner, Scott Sinclair and Micah Richards.
Manchester City: Hart, Clichy (Richards 46), Kolarov, Boyata, Rekik, Fernando (Garcia 46), Yaya Toure (Zuculini 46), Navas (Silva 46), Nasri (Guidetti 46), Dzeko (Milner 46), Jovetic (Sinclair 75).
Unused subs: Caballero, Rodwell, Wright, Huws, Leigh, Denayer, Iheanacho, Lawlor.