The world champions were far from their best in Dortmund on Sunday but Thomas Muller's double proved enough to seal the three points.
Muller handed the hosts the lead with 13 minutes gone only to see Scotland threaten to spring a shock when Ikechi Anya levelled midway through the second half.
It fell to Muller to put the visitors back in their place and Low - who watched his side lose a friendly 4-2 to Argentina on Wednesday - was just pleased to start with a victory.
"I'm happy with the three points," Low told the Germany Football Federation's website.
"It was important that we start with a victory. I had expected that it will be tough.
"A few individual errors after the break undermined us."
Germany's win had the potential to be soured by Marco Reus' late ankle injury, but Low revealed that the early signs were good.
"[It] seems to be not so bad. But we have to wait for the investigation," he added.
Germany captain Manuel Neuer felt that winning was all that mattered from the Group D opener.
"The most important thing was that we start with three points," he said.
"How doesn't matter. We have fulfilled our duty."
