Carlo Ancelotti wants his team to be fighting in all competitions come the end of the season.
Philipp Lahm made the most of Bayern Munich's preseason tour of the United States.
Mainz will be without Danish forward Emil Berggreen for up to six months after he tore cruciate knee ligaments in training.
Bundesliga teams have been warned not to field weakened teams against Bayern Munich in the coming campaign.
Gerard Deulofeu scored on a sharp free kick but Everton lost to Dynamo Dresden in their first game of the Dresden Cup on Friday night.
Bayern Munich captain Philipp Lahm sees no reason to be concerned by the team's preseason hiccups.