A dejected Kompany conceded that the whole team would need to take responsibility for the poor performance despite solid showings from some of the players, such as Raphael Guerreiro and Thomas Muller.
It was a day of calamities for the Bavarians which began with Serge Gnabry missing a penalty and was topped off by Joao Palhinha's sending off.
"We lost, no excuses," Kompany said after the match. "We can analyze as much as we want, but in the end we have to take responsibility for everything and make sure we build towards our next game. So far we always reacted well [to defeats].
"It's important to accept there will be criticism but we have to focus on the reaction in our next game."
Muller agreed, saying being down a player was not an excuse for playing poorly and that there would be a lot for them to go over in the analysis room.
"It was a football game with all facets," he said. "Of course, we did our part to ensure that things went our way at first.
"We played really well at the beginning, but then we made mistakes. We missed a penalty, got a red card and conceded goals.
"Just because you're down to ten men doesn't necessarily mean you're going to concede goals. There's something in it for all the analysts, and yet we have to put today's game behind us."
The good news for Bayern is that their nearest rivals in the Bundesliga standings, Bayer Leverkusen, were also defeated - 2-0 by Werder Bremen.
This means the Bavarians maintain their significant 19-point lead at the top of the table with just nine games of the season left to play.
Elsewhere in the Bundesliga on Saturday, VFB Stuttgart managed a 2-2 draw with Holstein Kiel despite being down to 10 men and Borussia Dortmund were beaten 0-1 at home by Augsburg.
RB Leipzig failed to beat Freiburg in a 0-0 draw despite dominating much of the game, while Wolfsburg and FC St Pauli played out to a 1-1 stalemate and Mainz were superb in the 3-1 dismantling of Borussia Monchengladbach.