The Greek side was bounced from the Champions League despite a win.
A 4-2 victory for Olympiacos over Malmo was not enough to propel the club into the last 16 of the UEFA Champions League.
The Greek champion required a win combined with a Juventus defeat to progress from Group A on Tuesday and took the lead after 22 minutes at the Georgios Karaiskakis Stadium through David Fuster's header.
A triumph for Age Hareide's Malmo would have seen the club qualify for the Europa League at the expense of Olympiacos and the team leveled midway through the second half thanks to substitute Simon Kroon.
The home side retook the lead via a superb Alejandro Dominguez strike, although Malmo - which had Enoch Adu sent off late on - again restored parity with 10 minutes remaining as Markus Rosenburg made it 2-2.
In spite of the setback, Olympiacos rallied to net two more goals courtesy of Konstantinos Mitroglou and Ibrahim Afellay to put the result beyond all doubt, but Juve's 0-0 draw with Atletico Madrid in Turin means Michel's side now drops into the Europa League.
Michel made nine changes to his team ahead of kickoff, with Pajtim Kasami and Fuster both handed spots in the starting lineup.
The Greek outfit would have been ahead after 10 minutes if not for Robin Olsen's superb double save.
After brilliantly parrying away Dominguez's drilled cross, the Swede somehow gathered Kasami's powerful close-range follow up.
Olsen could do nothing to prevent the home side taking the lead 12 minutes later when Fuster bravely latched onto Kasami's flick on to nod in at the back post.
The Spaniard received a trailing boot in the face from Pa Konate for his troubles, but recovered quickly enough as Olympiacos pressed for a second, with experienced playmaker Dominguez driving the club forward.
However, it was Malmo which came close to an equalizer with just over five minutes of the half remaining when a long throw from Ricardinho hit the crossbar after deflecting off the head of Olympiacos midfielder Delvin Ndinga.
Olympiacos started strongly after the interval and Olsen denied Mitroglou's close-range flick with yet another terrific save.
Despite the increased pressure from the home side, Malmo snatched a surprise leveler in the 59th minute when substitute Kroon slotted calmly past Roberto just two minutes after entering the fray.
Emil Forsberg broke swiftly down the right flank before curling in a pinpoint low cross to the feet of Kroon, who duly applied a deft finish into the bottom-right corner.
However, Olympiacos edged back in front just four minutes later through Dominguez's fantastic long-range strike.
The midfielder controlled the ball perfectly before executing a curling half volley that sailed past Olsen and nestled into the left-hand corner.
Malmo hit back with nine minutes left through Rosenberg – who grabbed both goals in October's clash between the two sides – as he connected with Anton Tinnerholm's cross before side footing home.
Olympiacos, though, made it 3-2 with just three minutes left when Mitroglou smothered home Dominguez's corner.
There was more late drama as the home side finally had a two-goal cushion when second-half substitute Afellay was played in by Kasami and the Dutch winger finished coolly past Olsen.
Malmo's evening then went from bad to worse when Adu received his second yellow card for a nasty-looking stamp on Kasami, who had to be carried off on a stretcher.