It proved to be a difficult start to the Euro 2016 qualifying campaign for the World Cup winners, but Muller, who scored both goals for the hosts in Dortmund, believes that it would have been foolish to expect anything less than a tough test from Scotland.
"I was not joking when I predicted a tight match," the Bayern Munich forward told reporters. "We studied the Scots a lot and they have not lost since they switched their coaches.
"They played compact football and we missed some chances to finish off the game. And when it is 1-0, it is tight against any team. I can live very well with this result and hopefully the fans do so, too."
Germany return to Group D action against Poland on October 11.