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Neuer described the Bundesliga champion's decision to relieve goalkeeping coach Tapalovic of his duties as "the most brutal thing I've experienced in my career".
The Bayern captain added that the departure of his mentor while he is recovering from the broken leg he sustained during a ski trip in December was "a blow – when I was already down on the ground".
Bayern CEO Oliver Kahn and sporting director Hasan Salihamidzic have made it clear they were not impressed with the Germany international's comments.
Hainer also criticised the long-serving Neuer on Monday.
"It is incomprehensible and disappointing for us that Manuel did not seek the way to us, but went directly to the public," he said.
"I'm even more disappointed than angry, because I would have thought that Manuel – who has been with us for so long – has so much trust and comes to us first to discuss it.
"I support one hundred per cent what Oliver Kahn and Hasan Salihamidzic said."
Hainer ruled out terminating Neuer's contract, but there are doubts over whether he will retain the captaincy.
"We will now sit down with him and work through everything calmly and professionally," Hainer said.
"The most important thing now is that Manuel gets well again and can play. And then we'll see."