The Bavarians needed an 90th minute penalty from Thomas Mueller, a controversial decision that referee Knut Kircher admitted later was a mistake, to edge past their opponents and maintain a perfect start to the season.
"We cannot allow that to happen," said forward Robert Lewandowski. "It will not be an easy game in Greece and the atmosphere there is fiery. We have to play very well from the start and not from the 46th minute as we did against Augsburg.
"We need to step more on the gas," the Poland striker said, with Bayern also due to play Dinamo Zagreb and Arsenal in Group F.
Bayern, who won the last of their five European Cups in 2013, will be without wingers Arjen Robben and Franck Ribery.
Douglas Costa, in fine form since joining them in the close season, is again expected to start on the left, with teenager Kingsley Coman also an option after the talented Frenchman came on as a substitute for his Bayern debut against Augsburg.
Central defenders Medhi Benatia and Holger Badstuber will also miss the game through injury with Javi Martinez likely to be included in the squad after recovering from a year-long ligament injury.
The Spanish holding midfielder was an unused substitute against Augsburg.
"We should learn our lessons from the Augsburg match because that should not happen," said Bayern captain Philipp Lahm. "We need to be able to turn on the switch."
Bayern's big name absences mean little for Olympiakos, who are well aware of the monumental task ahead.
"I do not think we should talk too much about the players missing because it makes no difference. There is so much quality in their squad," said Olympiakos defender Omar Elabdellaoui.
The Greek title holders, who have won their last six home fixtures in the Champions League, have also reinforced their squad, bringing in experienced former Argentina midfielder Esteban Cambiasso.
They are also on an 11-match unbeaten run in all competitions stretching back to April, which also included three wins out of three games in the Greek league this season.
"We need to focus on our work. We believe we can get something out of it because if you don't believe then you have already lost even before the game," said Elabdellaoui.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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