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The stunning result means Dortmund have now suffered three straight defeats at home in the Bundesliga for the first time since the 2013-14 season, when Jurgen Klopp was in charge.
Favre's future will come under scrutiny following this latest setback, despite steering BVB through to the last-16 stage of the Champions League.
The Swiss coach admitted his side - without the injured Erling Haaland - were masters of their own downfall, branding the display "very, very bad" while also praising their opponents.
"That was a disaster. It was bad," Favre told the media after the game.
"We weren't good at winning the ball. We made too many big mistakes. That's hard to explain. If you are not good at winning the ball, I mean the whole team, then you have a problem.