Bayern next meet either Manchester City or Lyon in the last four and are clear favourites to win the title for a sixth time.

“We feel good after this match, it was very special,” Muller said on BT Sport. “This tournament is special, it is a big statement but the nest game in the semi-final starts at 0-0, the statement doesn’t matter.

“I know the other teams watched our game and they can be impressed or not. It starts from 0-0 and we have to win the next game to reach our goal of playing in the final.

“We have to be quiet, we have to be calm and relaxed. We are very happy but tomorrow morning when we wake up and we answer the messages from home then we have to focus on the next game.

“That is our business. We are not here the quarter-final or semi-final, we are here to won the final. I know these tournament situations a lot and most of the time after these big wins it is more difficult so we have to be careful.”

This was not the greatest Barcelona side, but it was still a side with immense quality, but they were embarrassed defensively as Bayern could easily have hit double figures.

“It’s hard to explain, in this moment our team is in incredible shape,” Muller said. “We worked so hard, we work with this intensity and it is so hard for people to beat us. We had so much fun today.

“For our style of play it doesn’t matter who the names of the players are. Of course they have some special players and we have to be even more aggressive and come back again and again and again.”

Boss Quique Setien will surely pay the price for this embarrassment, coming after a limp end to their league campaign, and questions over the future of this side will be asked.

They had levelled at 1-1 through David Alaba’s own goal and then Luis Suarez got one back just before the hour, but there was to be no comeback.

Barcelona president Josep Maria Bartomeu has said decisions have already been made.

“It has been a very, very tough night. I am sorry for the Barça fans and members, for the players. For everyone. We were not the club that we represent, am so sorry,” he said on the club’s website.

“Here are some decisions that we had already made, and others that we will make over the next few days. Announcements will be made from next week, we need to make decisions after things have calmed down.

“Today is a day for reflection. Tomorrow we will try to raise our fans’ spirits following such a heavy defeat.

“It was a devastating result. I congratulate Bayern, they played a great game and deserved to go to the semi-finals. We were not up to the occasion, and we can only apologise to the members and fans.”

Defender Gerard Pique said: “I’m in pain. We all are. We can’t compete like that.

“It’s very, very tough to take. We must change the dynamic we are on. Is it an end of an era? I’m not sure but I know that we must accept that we have hit the bottom.”