The Germans claimed their eighth straight qualification victory, giving Low's side an unassailable 24 points at the top of Group A, with second-placed Turkey 11 points adrift.
"We have qualified for the finals at the earliest available opportunity," said Low, whose side travel to Poland for a friendly on Tuesday before taking on Belgium and Turkey in their remaining qualifiers next month.
"We must keep up the tension for the next few games. We have scored plenty of goals in qualification and only conceded a few. But if you attack as much as we do, you have to accept you are going to concede a few.
"We got caught out twice defensively, but I think we restricted the Austrians to just two chances and I prefer to focus on the fact that we created so many chances ourselves.
"It is our philosophy to constantly attack and we are working all the time to have a team in which we can interchange players. This is what you have to have if you want to be amongst the best in the world."
Real Madrid star Mesut Ozil believes the Germans are capable of going on to win the tournament next summer. "As a team, we put in a great performance and deserved the win," he said. "Our goal must be to win the EURO 2012 title, we know that we can do it."
Team-mate Lukas Podolski was in agreement. "That was a beautiful night of football," said the 26-year-old. "I have the confidence of the coach and I think I paid that back. We belong amongst the favourites and we obviously want to win the title."
Austria coach Didi Constantini, whose side cannot now qualify and whose contract expires in December, said the score reflected the gulf in class. "I think everyone saw there was a huge difference between Germany and Austria," he said.
"We were chasing the game in the first half. We had a few chances to make it 4-3, but Germany were simply too strong. I have a contract until 21 December and I intend on seeing that through."
Austria captain Christian Fuchs said his team got what they deserved, despite a battling display. "We made our lives difficult because we made too many mistakes in the build-up," said the Schalke defender. "Germany aren't the third best team in the world for nothing."