Antoine Griezmann was also sent back to title rivals Atletico Madrid on an initial loan amid a flurry of late activity in an attempt to help balance the books.
Barca's solid, if not spectacular, start to the LaLiga campaign, in which they have picked up seven points from a possible nine, helped lift the mood around Camp Nou somewhat.
Sergi Roberto was booed by a section of his own supporters when being substituted off during the game, which captain Gerard Pique admitted left him feeling "hurt".
With supporter unrest growing during a tough period for the LaLiga heavyweights, Laporta issued a video statement on his social media channels on Wednesday.
"Hello Cules. I am as disappointed and upset as all of you are," he said. "I need to tell you what is happening. This is one of the situations that we expected.
"I ask you all for your patience, and that you continue supporting our team. I also ask you to trust us, the people who are managing the club.
"We need your trust and time. Do not doubt that we will solve the situation."
Bayern's prolific striker Robert Lewandowski helped himself to a double after Thomas Muller had opened the scoring in the first half of Tuesday's Group E clash.
Barca have lost three successive home games in European competition for the first time in their history, having also lost to Juventus and Paris Saint-Germain at Camp Nou last season.
In their first European game since Messi's exit, the Catalans failed to register a shot on target in a Champions League match for the first time since Opta started recording such data in 2003-04.