Bayern presented Jan-Christian Dreesen as their new chief executive on Sunday, with president Herbert Hainer defending the decision to fire Kahn before the club lifted the Bundesliga title for an 11th consecutive season a day earlier.
Sporting director Hasan Salihamidzic was also dismissed on Saturday following the last-gasp 2-1 win over Cologne.
"Especially in the second half of the season, you could see that we weren't playing as we would have wished," Hainer told a news conference, adding there were also doubts about Kahn and Salihamidzic's ability to turn it around.
The timing and manner of the club's decision have overshadowed the celebrations.
It also takes attention away from the Bayern women's team's potentially title-winning game against Turbine Potsdam on Sunday.
Kahn said in a tweet that he was forbidden "by the club" from attending the team's game in Cologne or the trophy presentation in Munich, and he told Sky TV that "it was the worst day in my life, taking away being able to celebrate with the guys."
Hainer said both Kahn and Salihamidzic were informed of their dismissals on Thursday and while Salihamidzic took the news well and subsequently traveled to Cologne with the team, "unfortunately, it didn't go so well" with Kahn.
"It was very emotional and we couldn't agree with Oliver in the end that the finish would be amicable," Hainer said.
"Then on Friday we sat down with the supervisory board in the extraordinary meeting and decided to dismiss Oliver Kahn. And because of this situation, of course, he couldn't go [to the celebrations] on Sunday or to Cologne on Saturday either."
However, Kahn has given a different account.
"The claim that I freaked out when I was informed about the dismissal is definitely not true," Kahn said in a tweet on Sunday. "It was a calm and factual conversation ... On Saturday morning I got the message that I can't go to the game. I accepted this decision calmly. Of course I'm disappointed, but I'm really happy about this championship and I'm happy for the team, the coach and our fans."
Bayern had said before Saturday's match that Kahn was not in Cologne because he was sick in bed at home. Hainer said Sunday that was what Kahn had told the club.
On Saturday, Bayern coach Thomas Tuchel appeared unsure of his future following the dismissed of the men who had brought him to the club, but Hainer said Sunday he was certain the coach will continue.
"We had a very good talk and there no are thoughts [of leaving]," Hainer said. "I've no idea why Thomas Tuchel wouldn't be our coach."
Hainer said he will propose Tuesday at the club's shareholders' meeting that former chief executive Karl-Heinz Rummenigge be added to the supervisory board. Rummenigge was replaced by Kahn in 2022.
But the club still needs a replacement for Salihamidzic as sporting director.
Hainer refused to comment on speculation linking Eintracht Frankfurt's Markus Krosche or Leipzig's Max Eberl with the position, except to say both teams are in the German Cup final, where Bayern would like to be.
The 55-year-old Dreesen, who was vice-chairman of the supervisory board since 2014, hinted that he will take a more holistic approach than Kahn, who was known for his sometimes brusque manner.
"I'm firmly convinced that what happens on the field also reflects what's going on in the club as a whole. Everything around it is also a team," Dreesen said.
"When people enjoy their work and have trust in each other, it works better as a team and is more successful in the long term."
Bayern's Bundesliga win on Saturday was its 11th straight and a record-extending 33rd German championship altogether.