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Hansi Flick's side became the first team to hit eight goals in a knockout fixture, while the Blaugrana suffered their heaviest loss since 1951 afteran extraordinary 90 minutes in Lisbon.
Muller and substitute Philippe Coutinho grabbed doubles for Bayern, with Ivan Perisic, Serge Gnabry, Joshua Kimmich and Robert Lewandowski also getting in on the act, with a David Alaba own goal and a Luis Suarez strike proving to be nothing more than consolation efforts for Barca.
The match bore some resemblance to Germany's demolition of Brazil at the World Cup finals in South America six years ago, during which Muller was also among the scorers.
However, the 30-year-old claims Bayern were far more dominant against Barca, who were ultimately fortunate to escape with only a six-goal margin of defeat after beingexposed defensively.
"In 2014 against Brazil we never had the same control of the game," Muller said post-match.
"It was something that happened but let's not talk about it, let's talk about today. It was a special night, the result and the way we played was special.
"The best thing was to see that the players who came from the substitutes' bench hadthe same attitude and the same joy.
"The important thing is to do what we want on the pitch and for everyone to go to the limit."
The Bayern attacker added on how it feels to have beeninvolved in another historic game and the prospect of a semi-final showdown against either Manchester City or Lyon: "This is good, you can imagine how it feels, it was very special for us after this match.
"But we have to recover. It's a big statement but the next game, it starts 0-0. It doesn't matter.