The Greek side boast a 20-point lead at the top of their domestic league, but head into their two-legged Champions League last-16 tie as underdogs.
Although three-time European champions United boast a wealth of experience when it comes to continental competition, Michel expects his team, who finished runners-up to Paris Saint-Germain in Group C, to prosper in Athens.
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"The passion and mood we displayed to get here will guide us and we can create problems for United.
"Of course experience counts, but we have the capability to overcome the lack of experience. With all due respect to United, we will do everything in our power to beat them tomorrow night."
In contrast to Olympiakos, who have won 24 out of 26 league games this season, United have endured a disappointing season to date and sit sixth in the Premier League.
Yet Michel is not underestimating the quality of David Moyes' outfit, preferring instead to focus on his own club's preparations.
"United are top class and I will not comment about United's form. What's definite is that we will see the best possible Olympiakos," he added.
"The players are fully prepared. Our opponents are such a top club that we cannot afford to give less than 100 per cent. Our opponents are too big not to be at their best. We know what we can do.
"United cannot afford any mistakes given their position in the Premier League. This pressure may be a burden for the players.
"It may weigh too much on the players. We do not, however, know how it will affect their performance.
"We are in better shape than we were two months ago, [are] more experienced and have worked more and are better prepared. Our players are confident and psyched up."
Olympiakos midfielder Giannis Maniatis echoed his coach's comments, adding: "United have not been doing so well. But it will be wrong to say that they will be easier to beat.
"United are a huge and historic club that knows how to play these matches. We must be fully focused for 90 minutes. We respect them but we do not fear them.
"We have all been waiting for this for a long time. It is the match of the year for us."