The Greek Super League champions hold a 2-0 lead heading to Old Trafford on Wednesday, when a Champions League quarter-final place will be on the line.
Moyes' position at the helm has come under even greater scrutiny after his side's poor display in a 3-0 loss to Liverpool on Sunday left them seventh in the Premier League.
Michel sympathises with the former Everton manager's position but said his team had a job to do.
"David Moyes is not an enemy but we have opposite objectives," the Spaniard said.
"I don't like seeing any manager suffering.
"David Moyes is suffering as United manager. I have sympathy for all managers because I am one of them."
Goals from Alejandro Dominguez and Joel Campbell helped Olympiacos into their commanding lead in the last 16 tie.
Michel would love a similar result but expects to face a desperate United at Old Trafford, and said his team needed to do more than just try and protect their lead.
"We would like the game to go the same way as the first leg but we know it will be a different United," he said.
"(We expect) more determination and urgency on their behalf. We cannot just sit back protecting our 2-0 lead.
"We know the situation at United but this has nothing to do with us.
"All we have to do is play our game. We cannot rely on their difficulties. We must play to our advantages."
Michel said his players had nothing to fear, with the Spaniard more nervous than his squad.
"My players are not scared of anything. Maybe the manager is a bit more scared than the players," the 50-year-old said.
