The Greek champions hit the front just after the hour mark with Delvin Ndinga's header putting them 2-1 ahead at Juventus Stadium but Olympiacos could not hold onto their advantage for long with an own goal from goalkeeper Roberto Jimenez making it 2-2 four minutes later.
Paul Pogba then struck the winner for Juve almost immediately after the restart but Michel claimed a consolation prize in stoppage time when Roberto thwarted Arturo Vidal from the spot to ensure Olympiacos lead their Italian rivals on head-to-head for the rest of the group stage.
Olympiacos sit second in Group A after Tuesday's UEFA Champions League clash, just ahead of Juventus due to their away goals between the two teams - the aggregate score between them ended 3-3 with only Michel's side having scored on the road.
"I am very proud of my players. We showed what we are capable of," the Spanish coach said.
"Who knows, maybe that last save of Roberto [denying Vidal's penalty] might prove crucial and hand us qualification to the next stage."
Michel conceded his team did not start well in Italy with Andrea Pirlo giving Juventus the lead with a direct free-kick in the 21st minute.
But Olympiacos equalised just three minutes later through Alberto Botia and Michel argued his team were up to the level with Juventus for the rest of the contest.
"We had a tough time settling into a rhythm in the early stages of the match but after equalising we improved a lot and I am perfectly satisfied with my players' efforts," he said.
"We created several chances to get a point but let's not forget that our rivals were Juventus."
