The encounter in Salvador was settled by a goal from the 2010 Golden Boot winner, a result that puts the three-time World Cup winners through to the knockout phase in Brazil.
"We were dominant," Mueller told FIFA.com. "All the Americans did was sit back deep in their own half, and when that happens, it just becomes a patience game.
"It was an okay game from us... We may only have won it 1-0, but we can take that too."
The USA are also through despite their defeat, with Portugal and Ghana heading home.