Germany launched an onslaught with a flurry on first-half goals, with Muller opening the scoring before Miroslav Klose, Sami Khedira and two from Toni Kroos left the host trailing 5-0 at halftime.
Andre Schurrle added two more after the break and, though Oscar managed to grab a consolation for the Selecao, Muller could not disguise his shock at such a remarkable victory.
"Of course, you couldn't expect that," the 24-year-old told ZDF. "That shows how different games can be. Brazil played differently than defensive teams and we took advantage of this in an extraordinary way. It was just crazy."
However, as Germany looks forward to a final against Argentina or the Netherlands at the Maracana on Sunday, the Bayern Munich forward urged his teammates not to get carried away.
"You should keep a sense of proportion," he said. "Every match is different. Just like everyone talked us down after the match against Algeria, they will hype us now. We are a squad with big quality, with an awesome team."
Muller's words were echoed by Miroslav Klose, whose goal allowed him to surpass Brazil's Ronaldo to become the World Cup's all-time top scorer with 16 — although he abstained from his traditional somersault celebration.
"We had a great start," the 36-year-old said. "You can see in training that we can play together. We really are a unit. It is important that set pieces work, you could see that today again when we scored the first [following a corner]. Toni passes the ball where it needs to go — that's a real strength.
"I did no flip [after my goal] because someone kicked my foot when I shot before."