"The most important thing was the victory for the team, but I'm very happy with the two goals I scored," said Ozil.
"I enjoyed being on the pitch and a game like this is good for me to keep building my confidence.
"The football year has just started, but I feel good and I think I can keep improving. [Real Madrid] have a long season ahead of us and I want to be a very important part of it."
Germany are away in Austria in their next Group C fixture on Tuesday.