Despite being on the back foot for much of the game, Olympiacos took a first-half lead through the Greece international, who struck twice more after the break to hand Michel’s side their first win in Group C.
And the quality of Mitroglou's performance was not lost on his manager, who was delighted by the clinical nature of his whole side's showing.
"To win 3-0 away is not a result one expects in this competition. We played well and managed to make the most out of our opportunities," Michel said.
"It was Mitroglou’s night, but I have to sing the praise of all players. Roberto (Jimenez) made some fantastic saves tonight and everybody made a huge effort."
The result means that Olympiacos have moved into joint second of the group with Benfica, who lost 3-0 at leaders Paris Saint-Germain.
