My header was not intentional, says Muller
Muller's double secured all three points for Joachim Low's side in Dortmund on Sunday but the world champions were made to work hard in their opening Group D clash.
The forward – who scored five goals at this year's World Cup – gave Germany the lead with a looping header that he later acknowledged was not intentional.
Ikechi Anya drew Scotland level in the 66th minute but parity lasted just four minutes before Muller struck again.
Muller said: "Making it 2-1 was a joy, because I know how important those three points are.
"I could have scored the opener with a header earlier.
"Football is football – you try your best, but I did not intend to place the header [for the opening goal] where it went.
"I just tried to win the aerial challenge against this towering Scotsman [Russell Martin]."
Germany defender Benedikt Howedes felt his side deserved their win on the basis of their first-half dominance.
"It was hard work today – a difficult win," Howedes said.
"But against a strong Scottish side, that was no less than we expected.
"The first half was a one-way street. In the second half, they got a bit braver, invested more in attacking and equalised.
"It was good that we made it 2-1 shortly afterwards."