The Black Stars became only the third African side to advance to the last eight of a World Cup, enjoying a large section of home support as the continent's last representatives at the first African World Cup.
But Rajevac insisted after the drama-filled extra-time victory that his side's attractive playing style was winning fans from an area much wider than across Africa.
"The whole world is watching these games. This is the World Cup we are talking about. Everybody loves good football and I think because of that Ghana has the support of the whole world and not only the African continent."
Rajevac, an unheralded Serbian coach when he arrived in Ghana just over two years ago, said being the only African side left at the tournament did not impose an unnecessary burden on his team.
"The players showed they are a team who concentrate on what happens on the pitch. There are no other pressures."
He looked to deflect persistent questions about the team's new-found position as flag bearers for African hopes.
"Now, we are going to get ready for the match against Uruguay. There is lots at stake."
Ghana play Uruguay at Soccer City in Johannesburg on Friday in the second of the quarter-final matches.
The previous African teams to reach the last eight are Cameroon (1990) and Senegal (2002).
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