Die Mannschaft booked their place in the last four of the competition with a slender 1-0 victory over France at the Maracana, to secure a fourth straight semis appearance.
Neuer was called into action late on to deny Karim Benzema, whose shot was well kept out by the Bayern Munich keeper.
"It was just instinctive, it comes naturally," the 28-year-old is quoted as saying by Sky Sports News of the save.
"Of course, to be able to play in this stadium, and it being a World Cup quarter-final, and then to put in this performance on top - it's all worthy of a place in the semi-finals.
"We played good football and wanted to get through, and now we're looking forward to our next game."
A meeting with Brazil or Colombia awaits Germany in the semi-finals.