The USA scored in the first and 86th minutes to triumph at the Arena das Dunas, as Ghana missed out on points despite Andre Ayew's equaliser with eight minutes remaining.
Clint Dempsey gave the USA the lead when he burst onto Jermaine Jones' pass, cut inside John Boye and slotted home the opening goal after just 29 seconds, while the Americans claimed victory with John Brooks' header in the closing stages after he got away from the same Ghanaian defender to power a corner into the net.
Appiah's men dominated the Group G fixture at the FIFA World Cup with 456 passes to the Americans' 276, while Ghana had 21 shots to eight but lacked the defensive composure to get a result.
"I think that early goal was a disaster, it was unfortunate," Appiah said post-match.
"Loss of concentration cost us big time. All I can say is that it was a very tough game and when you play at this high level any little mistake can cost you dearly.
"We had a lot of the ball and created a lot of chances, but we didn't make the most of our chances, but USA took theirs."
Ghana have advanced from their groups at each of their previous World Cup appearances; reaching the round of 16 in Germany eight years ago and the quarter-finals in South Africa in 2010.
But having lost their opening game in Brazil, a round of 16 berth looks unlikely for Ghana, considering only 8.6 per cent of teams that have suffered defeat in their first group game over the past four tournaments have managed to advance.
Appiah was well aware of the enormity of his team's challenge, as he looked ahead to fixtures against Germany and Portugal.
"It's not going to be easy to qualify for the group but we'll give everything to do just that," the 53-year-old said.
"We're going to have to play well against Germany and I know we'll give them a good game."
