The Black Stars fell behind in the first minute to Clint Dempsey's strike and, though they levelled through Andre Ayew late in the game, Jurgen Klinsmann's side sealed a 2-1 win through John Brooks' header four minutes from time.
With Ghana still to play Portugal and Germany, they face a struggle to progress beyond Group G, a reality Boateng freely accepts.
"We know that we need to win now," the 27-year-old told the DFB's official site.
"And we also know that there will be no easy task against Germany. But we will prepare and try to give our all for it.
"The first game is always the most difficult and somehow always the most important and we just went to sleep. We must not now hang our heads - we have another game in four days."
Boateng, who has 12 caps and two goals for his national side, faced stern criticism in Ghana when he retired from international football in 2011 - only to reverse his decision two years later - but was dismayed by coach Kwesi Appiah's decision not to start him against the Stars and Stripes.
"Yes, I was surprised that I did not play from the start," he complained after coming on as a substitute in the 59th minute.
"Apparently the coach had different ideas."
Commenting on the exclusion of Boateng and Michael Essien in the starting line-up, Appiah defended his tactical approach, but conceded that his team now face a difficult battle to qualify for the second round."Kevin and Michael are good players," he said. "But I opted for a 4-4-2 and found that Jordan Ayew and Asamoah Gyan worked well in training.
"The early goal for us was a disaster. Now we need two wins to still qualify for the knockout stages, even if it is difficult."
Ghana face Germany on Saturday in their second Group G game.