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Despite suffering a 1-0 defeat by Germany on Wednesday, Ghana still went through to the knockout stage as Group D runners-up where they will face the Americans, who won Group C after beating Algeria 1-0 on Wednesday.
Ghana now look to be Africa's sole representative in the last 16 in the first World Cup played on African soil, barring a near-miracle from the Ivory Coast in their final match on Thursday.
"To qualify is really very important for us and for Africa," said Rajevac.
"I am really very emotional and moved. I hope we can benefit from the support of all of the South Africa people and the continent of Africa.
"It's not really the time to rejoice over qualifying because of the match against the USA. We don't have much time."
Ghana were slayed by a super strike from Germany midfielder Mesut Ozil from the edge of the penalty area on the hour mark which proved decisive while Australia's 2-1 win over Serbia in the other Group D match was academic.
Ghana defender Hans Sarpei, who plays in the Bundesliga for Bayer Leverkusen, said his side face just as tough a battle against a USA side buoyed by their late win over Algeria, than if they were facing Fabio Capello's England who instead play Germany.
"We are in the next round and we are happy with that," said the 33-year-old veteran.
"Of course it was a defeat and the mood is a bit flat, but we are glad, nevertheless.
"Only dear God maybe knows why we will play now against the USA, but I don't know whether this game will be any easier than if we had played England."
For midfielder Kevin-Prince Boateng Wednesday's match was an emotional occasion against the country of his birth, especially with younger brother Jerome playing for Germany
The brothers, born in Berlin, are feuding after Kevin-Prince's tackle on Michael Ballack in the FA Cup final between Chelsea and Portsmouth ruled the Germany captain out of the World Cup with an ankle injury.
"It was already something special for me to to play against Germany," admitted the 23-year-old Portsmouth star. "I have thought the whole day about that."
