Bayern won 6-4 on aggregate after a 4-3 victory at the Allianz Arena on Wednesday, with Eduardo Camavinga's late red card a turning point.
Players mobbed referee Slavko VinÄiÄ at the final whistle and Arda GĂŒler was sent off near the tunnel for his protests, earning a suspension for next season's Champions League.
Welt described the post-match scenes as exposing a deeper cultural problem at the club. "Conspiracy theories have long been part of the DNA of a club that, for years, has been losing all respect and dignity. Winning is easy, but few know how to lose. Real Madrid is not one of them."
The article pointed to Camavinga's dismissal directly. "He, who had already received a yellow card for a clear tactical foul, should have refrained from this kind of antics at all costs.
"That his teammates saw things differently may also be due to the fact that disloyal behaviour, intimidation of referees, and backstabbing legends have long been part of Real Madrid's DNA."
Sport Bild echoed those views and singled out VinĂcius JĂșnior. "When Luis DĂaz scored the equaliser, the ever-provocative VinĂcius Junior was already applauding contemptuously in the referee's direction."
The magazine called for the departure of the club's more divisive figures. "It would be desirable for some oversized egos to leave the club. Only then can the club become the best in the world again and, above all, a more beloved club."
Real Madrid are nine points behind Barcelona in La Liga and face a second consecutive trophyless season.