The Germans were frustrated by a tight Portuguese defence on Saturday and had to wait 72 minutes before Mario Gomez headed in the only goal after the Portuguese defence failed to clear Sami Khedira's cross.
Until then, the three-times European champions, among the tournament favourites, had less than a handful of scoring chances and it was Portugal who twice hit the woodwork.
"This opening win can given the team an initial spark for the tournament, it gives us more confidence. But we need to improve on certain things, though. We need to create more scoring chances, because the tournament has now begun," said the 52-year-old Low.
"It is not like the World Cup where you can have a sort of warm-up game [against a weak team]. Here you start at 100 percent like in Formula One, only without a warm-up lap. You can't start the tournament chasing after the music."
The Germans take on Netherlands in their next Group B game in Kharkiv on Wednesday with the Dutch facing a possible early tournament exit after their surprise 1-0 defeat by Denmark.
"I would have preferred if they had drawn their game. They are now with their backs to the wall and have to play an all-or-nothing game. That makes that match even more exciting," Loew said.
Germany's victory will have no doubt eased their nerves after a less than ideal pre-tournament preparation in which many players joined the squad late.
Among those feeling more confident is holding midfielder Bastian Schweinsteiger, injured for much of the year.
"It was extremely important that he was on the pitch. He had played a lot towards the end of the season. Together with Sami Khedira he was ever-present in midfield."
