Their four-game stretch without a Bundesliga victory also coincides with a five-game scoreless streak from Mane, the former Liverpool man's longest baron run in 2022.
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The defeat followed draws against Stuttgart, Union Berlin and Borussia Monchengladbach, leaving Bayern fifth in the table heading into the international break, with 12 points their fewest after seven games since the 2011/12 season.
Mane had a chance to open the scoring early on when he was played through one-on-one with opposition goalkeeper Rafal Gikiewicz, whose perfectly-timed tackle denied the chance, and that soon became the theme of the game.
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The Pole thwarted a number of attempts throughout the match, and in an act of desperation, Bayern coach Julian Nagelsmann threw his opposing no.1 upfield, with Neuer almost scoring with one of his two efforts.
The German shot-stopper drew the best save of the game from Gikiewicz who brilliantly kept out his goal-bound header, leaving Nagelsmann without answers post-match.
"I'm sorting my thoughts," the shocked 35-year-old said in the aftermath.
"When I look at the statistics, it's basically the case that we have to win the game.
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"We let a lot of chances flow out of the stadium in the first and second half - with a lot of superior numbers, with a lot of space behind the defence.
"With simple one-on-ones we could have used the space well, but we gave away a lot of manpower and played very laissez-faire in the last third."
Asked specifically about Mane's lack of goals, the manager added: "I'm not talking about individual players now, I'll do that in the dressing room."
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Nagelsmann was also asked if he was missing Robert Lewandowski, who has eight league goals for Barcelona this season, twice the number of Bayern's top scorer, Jamal Musiala.
He replied: "What does it matter if I say no? And what does it matter if I say yes?
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"We substituted the classic nine [Mane] with [Eric-Maxim] Choupo-Moting today and we don't have another one. It doesn't really matter what I answer now.
"If I say no, then you will say 'He doesn't see the problem,' If I say yes, then everyone writes: 'He misses Lewandowski'."
Bayern now head to Oktoberfest in Munich, which is normally a cause of celebration for the Bavarian giants, but this year the mood is solemn.
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Asked how he will spend his time off, Naglesmann replied: "I think about everything - about me, about the situation, about everything."
The mood was matched by CEO and club legend Oliver Kahn, who defended his manager and criticised the players concentration.
"I think that we are working out a wealth of opportunities and scoring far too few goals," he explained. "We simply cannot make the punch at the end.
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"The opponent can always clarify [finish clinically] again and again, the last pass is played too sloppily again and again, there is a lack of the necessary concentration.
"We are now on an international break, so we will take our time to take a look at everything. Also analyse. Have a lot of talks. And see that we can get back on the road to success as quickly as possible.
"We'll get to the bottom of it all. We're not dealing with any other coaches now, we're convinced of Julian."
Rumblings are already beginning in the German media around recently-sacked former Chelsea manager Thomas Tuchel.
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Media giants BILD report that the Champions League winner is 'much appreciated' by Bayern's hierarchy, and Nagelsmann has a 'kick-out' clause in his contract, meaning the incumbents time off will include plenty of introspection.