Thomas Muller's second-half strike proved enough to see off the Americans, and Low believes that his side were worthy victors.
"We were well organised and dominated the match," he told reporters. "We didn't let USA have a chance on our goal right up to the final whistle.
"We were strong in midfield and that's where we put them under pressure. Bastian Schweinsteiger was excellent until he ran out of steam. It was a good opportunity to give Sami Khedira a rest."
He added: "Now we're in the round of 16 and it's a different kind of situation. It's all or nothing and that brings with it a completely different dynamic and a different kind of tension."
Germany will take on Algeria in the last 16 of the competition.