Arturo Vidal launched a scathing attack on referee Viktor Kassai, claiming he led to Bayern Munich's elimination from the Champions League as the Chilean midfielder was left doubting the legitimacy of football.

Bayern suffered a 4-2 loss to Real Madrid after extra time in the second leg of their quarter-final tie on Tuesday as the titleholders progressed to the final four 6-3 on aggregate following Vidal's controversial sending off.

Kassai was at the centre of the controversy in the Spanish capital, showing Vidal a second yellow card for what appeared to be a fair challenge in the 84th minute before the Hungarian official allowed Cristiano Ronaldo to complete his hat-trick in extra time, despite strong calls for offside.

And Vidal was less than impressed with Kassai's performance at the Santiago Bernabeu.

"This robbery cannot happen in the Champions League, it was clearly noticeable and it starts to make you doubt [the game] a bit," Vidal said.

"We wanted to qualify and this gives us a lot of rage, that a match of such intensity can be decided by the referee.

"He was very wrong and that has knocked us out of Europe.

"When they embarrass you in this way it's very strong and it creates a lot of rage."