The Die Mannschaft earned a hard-fought 2-2 draw against minnows Hungary on Wednesday to finish second behind France and book their place in the knockout rounds.
Germany had to twice come from behind to earn a point, with substitute Leon Goretzka’s strike sparring Low’s blushes with six minutes to go.
Germany’s reward for finishing second is a date with England at Wembley in what will be a repeat of the EURO 1996 semi-final, which the former won on penalties.
Having picked four points from the ‘Group of Death’, there is still room for improvement from Germany, and Low who will leave his role as manager after the tournament, is optimistic that his side will be better prepared for the knockout rounds.
"We had an extremely good attitude; we made mistakes, but we fought," Germany head coach Low told reporters.
"It wasn't a game for the faint of heart. We knew that Hungary would give everything and that it would be as close as it was.
"To get through this group in the end, that was good and that was the goal. France also only drew 1-1 against Hungary, the so-called little ones gave everything. It wasn't easy, they had nothing to lose.
"But in the end what counts is that we are through."
He added: "This is an absolute highlight when you can play against England at Wembley.
"We will be well prepared and we will perform differently, I can promise.
"It's great that we got through in this tough group."