Prior to the World Cup, many Ghanaian players had stated that their objective is to compete for the prestigious title.
After Sunday's game, Gyan said the 2010 African Cup of Nations runners-up are determined to extend their winning streak in the quadrennial tournament.
"It was a difficult game but we really wanted to win and we made the coach happy. This is just the beginning and we are going to build from this," he said
"There is good team spirit with the senior players helping the younger players.
"South Africa is behind us and South Africa is behind all African teams. We will do our best to make South Africa and Africa proud.
"This win is very important. We took the three points and everybody is happy.
"We knew what the Serbians would do. They play a long ball but tactically we were perfect today."