The Germans took a long time to hit their stride against a similarly uneasy Portugal before Mario Gomez buried a 72nd-minute header to give then a 1-0 victory.
"It was a good goal for Mario and for the team. We won and that's the important thing," Low told German television.
"We were a little tense in the first match, after hearing Denmark beat the Netherlands. No team wants to get behind in the first match. You get a bit of a spark if you win the first match and that's what we wanted."
Netherlands lost 1-0 to an unfancied Denmark side, as they consistently failed to turn chances into goals.
"We started in this tournament with music but we have to improve. We will have to attack with more focus but I am confident we will succeed in doing that," Low said.
He replaced Gomez with Miroslav Klose, who was celebrating his 34th birthday on Saturday, in the 80th minute.
FRESH LEGS
"The switch was planned. Mario worked hard at both ends. He was worn down a bit and [we] needed some fresh legs. Mario made the goal so we waited a few minutes to make the switch."
Low also praised Jerome Boateng, criticised in the German press for his recent late night out on the town.
"Jerome had a good match. He won quite a few battles and did a first class job."
Sami Khedira, who crossed for Gomez to score, said they were flagging towards the end of the match.
"It was a very important match, the start of the tournament. We were running out of steam a bit towards the end... they were well prepared for us and I think that's the way it's going to be through the whole tournament, offensive and quick football.
"That is the way we are going to have to play in this tournament too."
Germany play Netherlands on Wednesday in Kharkiv.
