Bayern Munich has singled out Hungarian referee Viktor Kassai as the decisive factor for its Champions League quarterfinal exit to Real Madrid.

"I have to say, I'm filled with unbelievable rage for the first time today. Rage, because we were swindled. Swindled in the truest sense of the word," Bayern chairman Karl-Heinz Rummenigge said in his post-game dinner speech, after Tuesday's 4-2 loss in Madrid saw the Spanish side progress 6-3 on aggregate.

Kassai made a number of debatable decisions, but Bayern's anger was focused on his sending off of Arturo Vidal for a second yellow card in the 84th minute, even though the midfielder appeared to get the ball as he challenged Marco Asensio, and on the awarding of two Cristiano Ronaldo goals that were subsequently shown to be offside.

Rummenigge likened the manner of the defeat in Madrid to that against Manchester United in the 1999 final after two injury-time goals, and to the loss against Chelsea on penalties in the 2012 final in its own stadium.

"I think everyone was a witness to a game that wrote history today," Rummenigge said. "(Bayern president) Uli Hoeness and I, we've taken many blows. Today was also such a game."

Bayern coach Carlo Ancelotti also criticized the referee's performance after the game, while his players were unanimous in pinning the blame for the defeat on Kassai.

"When Madrid got scared, the referee began his show," Vidal said. "He knocked us out."

Thomas Mueller said he found it difficult to blame a referee for a defeat "but today there's no way around it."

Winger Arjen Robben said, "it's such a shame that such a super game, such a top game, is decided by one man with a whistle."

Defender Mats Hummels said the decisions "hurt," while Jerome Boateng said, "10 against 14 is hard to play. They were decisive scenes."

Robert Lewandowski was also incorrectly pulled back for offside when Boateng sent a long ball through for what would have been a good chance for Bayern.

Spanish media reports say Vidal, Lewandowski and Thiago Alcantara were so incensed, that they followed Kassai to his dressing room to complain after the game, although that has been denied by Bayern.

However, no Bayern players spoke of the decisions that helped their side on the night. Vidal was fortunate not to have been shown his second yellow card earlier, in the 48th minute, for a challenge on Casemiro.

The penalty that was awarded to Bayern, when Robben went down under Casemiro's challenge, was not clear-cut, and two Bayern players were offside as Madrid captain Sergio Ramos scored an own goal in the 78th.

Ancelotti made the case for video technology immediately after the game, saying the mistakes were unacceptable for the Champions League quarterfinals.

Bayern's misery was compounded with the news goalkeeper Manuel Neuer suffered a fracture to his left foot as Ronaldo scored his third goal, ruling him out for the rest of the season.

The 31-year-old Germany goalkeeper had been instrumental in denying Madrid a host of chances over both legs. In Tuesday's second leg alone, Madrid had 12 attempts on target, compared to two for the visitors.

"Madrid is not undeservedly through. You have to say that," Hummels acknowledged.