The Bayern Munich attacker netted three times as Joachim Low's side got their campaign under way with an ominously ruthless 4-0 win over Cristiano Ronaldo and co.
Mats Hummels also found the net as Germany backed up their status among the pre-tournament favourites in impressive fashion.
"Three goals in the opening game, that is of course wonderful," he told ARD. "Each one was more beautiful than the last.
"In the blazing sun, it was extremely difficult, especially without the ball.
"When you go ahead after 12 minutes, it is naturally reassuring and we countered extremely well."
Muller was also involved in the game's controversial flash point when Pepe saw red for headbutting the Bayern man.
"I felt the impact of Pepe, whether it is a red or not is not for me to decide," he explained.
"I was not trying to buy a red card."
