Thomas Muller has hit out at referee Viktor Kassai and his assistants in the wake of Bayern Munich's controversial Champions League exit at the hands of Real Madrid, saying the game was 10 against 14.

Bayern were 2-1 up after 90 minutes, taking the game to extra time after their loss by the same scoreline at the Allianz Arena last week, but Madrid decided the tie with three more goals to send the Bavarians packing.

The game was marred by a number of questionable refereeing decisions, though, as Kassai dismissed Arturo Vidal for what seemed like a fair challenge, before Cristiano Ronaldo scored two goals from offside positions.

"We did not put in a perfect performance, but we acted like men on the pitch if you look at the way the game developed," Muller told reporters.

"If you look at the way things went, it is extremely difficult when you are playing with 10 against 14... The 2-2 was the worst, the assistant referee had a clear view. That killed us.

"We were in great shape mentally after we went 2-1 up and still had 11 players on the pitch. But then the referees took the wind out of our sails. You cannot just go home and say 'things like this happen' after what happened here.

"Arturo could perhaps have been dismissed before, but definitely not in the situation where he got his second yellow."