Bayern secured a record 10th straight league title with Klassiker victory over Borussia Dortmund last weekend but was caught cold by Mainz after first-half strikes from Jonathan Burkardt and Moussa Niakhate.
Robert Lewandowski reduced the deficit with his 18th away league goal this season, setting a Bundesliga record for a single campaign, while taking his tally to 49 in all competitions – the most of any player in Europe's top five leagues.
Leandro Barreiro Martins restored the two-goal cushion after the interval for Bo Svensson's hosts as Mainz coasted to just a second league win over an uncharacteristically poor Bayern in its past 10 attempts.
Nagelsmann expressed frustration with his side after the defeat but acknowledged a downturn in performance was to be expected after the title win.
"We had too many performances and defeats of this kind this season," he said.
"I have an explanation for it, but I won't give it to you. It's not for the media. I say it internally.
"After winning the 10th title in a row, it's a bit human but we still have to play for the badge on our chest.
"It seems like the passion isn't really there anymore. We reached a point where something needs to change. That's where we are right now."