Arsenal and Manchester City both lost their final group games in this season's Champions League.
Substitute Costas Mitroglou fired Olympiakos to a 2-1 victory over Arsenal, as the Greek champions came from behind with two goals in nine minutes.
Arsenal took the lead in the 38th minute with Tomas Rosicky, set up by Gervinho, who outran two defenders and skillfully swung the ball back.
Yiannis Maniatis equalised in the 64th minutes after pouncing on a defensive error before Mitroglou scored the winner in the 73rd minute.
Arsenal had already qualified from Group B, while Olympiakos were already destined for the Europa League.
City finished bottom of Group D and failed to quaify for the Europa League after losing 1-0 to Borussia Dortmund. Julian Scheiber scored the only goal in the second half