The team's defense was excellent and he was very happy with the attacking play, Loew said, but he felt Germany's youngest World Cup squad for three-quarters of a century could have closed down spaces in the middle of the field better.
"This was the first match of our tournament and we know that Australia is not going to be the ultimate benchmark," Loew told a news conference.
"There will be more difficult opponents to play. So this was a good warm-up. We will be happy about this win," he said.
Germany face Serbia on June 18 and Loew said they could provide stiffer competition, given they lost to Ghana Sunday and will need to win to get their campaign back on track.
"Serbia lost today, so they will be quite a different benchmark," he said.
"What we need to do is remain focused," he added.
Loew defended his decision to play Lukas Podolski and Miroslav Klose, despite their goal drought last season. Both came through for their coach, each scoring to put Germany 2-0 up by half time.
"I didn't have to stick to these players, they didn't have to deliver on any promises," he said.
"I simply know that I can fully rely on these players even though they might not score in one match, even if they go through a bad patch. I have full confidence in them," he added.
Australia's resolute and well-organized defense had been expected to pose problems for the German attack, but Loew said he told his players to focus on pushing low balls forward to create gaps -- a tactic that paid off well in the game.
"The way we set up our attacks, the way we passed balls to and fro, is something we have been working on very intensively," he said. "We tried to play long straight passes ... and keep the ball low. And that created problems for the Australians."
"Everybody expects things to kick off nicely and well after a long preparation so we can be happy and confident," he said.
"We want to reach the round of 16 at least so we can be satisfied," he added.