Ghana are the only African nation left in the tournament and only the third side from the continent to reach the final eight.
"I am the happiest man in the world," Gyan said after sealing a clash against Uruguay at Soccer City Stadium in Johannesburg on July 2.
"In 2006 we made the second round, now we have gone a step further. We've made everybody proud. Not Ghana alone, but all of Africa."
Ghana midfielder Andre Ayew reiterated Gyan's wish to carry the torch for the host continent and said: "We had to fight to the last second and we gave our all. We fought for the continent and for Ghana. We hope the whole African nation is proud.
"Everything is possible. We are very tired but we have five days rest and will focus for the next game against Uruguay. They have great strikers but if God is behind us anything is possible.
"We were disappointed there was no African team with us. We need to make the whole continent proud and we feel we have the whole continent behind us and that gives us energy.''
USA boss Bob Bradley described the loss as "a stinging, tough defeat" and said that his side, which battled back to cancel out Kevin-Prince Boateng's opening strike, just couldn't do it a second time after Gyan's goal.
"We had already expended a lot of energy at that time," Bradley said. "I think we put ourselves in trouble with giving up the early goal again."
Meanwhile, Ghana coach Milovan Rajevac believes his side's World Cup adventure is far from over and is hoping to reach the semi-finals with the Black Stars.
Rajevac said: "Ghana are now among the eight best teams in the world. This is fantastic. When we reached final of the African Cup the boys learned how to compete. That is the most important thing and I now hope Ghana will go further.
"The whole world is watching these games. Everybody loves good football. Ghana has the support of the whole world because it is the only African country still playing at the World Cup."