Germany, who have also reached the last four of the previous two European Championships, strolled through thanks to Mats Hummels' 12th-minute header at the Maracana.
Low, the Germany coach since 2006, said afterwards: "It's quite a record - our president told me we have won 28 out of 31 official matches so that's quite a performance.
"This team has intrinsic qualities, is solid and stable and since 2010 we have taken on board new players like Mats Hummels - we have invested a lot."
Low believes their Latin American opponents Brazil will start with an advantage in the semi-final in Belo Horizonte however.
He added: "They will have a home advantage, you can't deny that. The South Americans are fighting for their lives here."
Low revealed that he had spoken to Per Mertesacker on Friday night to explain why he was being dropped to allow for Hummels' inclusion - the Arsenal defender has long been a stalwart member of his teams.
He said: "Per is very important player for us and I spoke to him last night and explained, and he had a marvellous attitude and said 'I just want to help the team'.
"I chose Jerome Boateng and Mats Hummels for tactical reasons - we had seen France's players Valbuena and Griezmann attack with great speed and I thought I would be able to solve that problem."