The Bayern manager said the official's performance was "worse" than that his team's after a questionable second yellow card for Arturo Vidal on 84 minutes, and two Cristiano Ronaldo goals that probably should have been ruled offside.
But the game was marred by some dodgy refereeing: Bayern's Viktor Real was sent off and two of Ronaldo's goals in extra time were clearly off-side.
With the game heading towards extra-time Vidal was sent off for a second booking after appearing to win the ball cleanly from Asensio, leaving Bayern with 10 like in the first leg when Javi Martinez was dismissed.
But despite having the momentum, they were at the distinct disadvantage of having to play extra-time with 10 men, and eventually crumbled to Madrid's might.
"They have told me their second goal was also offside", said Zidane. He scored 3 goals.
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Those strikes, along with Arturo Vidal's harsh red card, proved the game's decisive moments as the momentum swung back to the home side.
And Asensio sealed victory in sensational style with a stunning solo run and low right-footed finish as many Bayern players sank to their knees knowing Champions League glory had passed them by for another year. We wanted to go through and there's a lot of anger in that a match of such intensity is decided by the referee.
Lewandowski scored first via penalty in the 53rd minute, after Casemiro fouled Arjen Robben in the Madrid box.
"To score six goals against a team like Bayern Munich isn't easy, so we deserved to go through", added Ronaldo. The Spanish defender was making his 100th Champions League appearance.
Carlo Ancelotti's Bayern began well, with Thiago Alcantara's close-range shot brilliantly blocked on the goal line by Marcelo. In trying to snuff out Lewandowski after substitute Thomas Müller had helped the ball along, the ball bounced off the Real Madrid captain and creeped into his own net.