The former Bayern boss feels the board should have avoided to openly oppose the sporting director following his criticism of the team's performances
The club's sporting director had openly slammed the team's lack of passion after the 2-0 win over Hannover, prompting critical responses from their president and chief executive.
"I was surprised that Uli Hoeness and Karl-Heinz Rummenigge criticised Matthias," Hitzfeld told Sky.
"It wasn't good to do that in public, because that way Sammer is losing some of his authority. However, I can imagine that Sammer didn't talk to Pep Guardiola about the matter beforehand.
"Guardiola does not like this, because he's very protective of his team.
"Sammer stirred up a hornet's nest. Rummenigge and Hoeness wanted to set an example, the board wants to protect the coach."
Hitzfeld also commented on the unusual pairing of Philipp Lahm and Bastian Schweinsteiger in the defensive midfield since the arrival of the Spanish coach.
"I can only think of it as a temporary solution. Pep wants to keep up the focus of his players and looks for alternatives in case something happens.
"[Javi] Martinez is injured, Thiago [Alcantara] is injured, Schweinsteiger isn't fully fit.
"Schweinsteiger, however, has reacted superbly. He is one of the best players in the world anyway. At the moment, Bayern can't do without Schweinsteiger."