With Ivory Coast needing a huge turnaround in goal difference to qualify from Group G and with Cameroon, Nigeria, Algeria and hosts South Africa already eliminated, Ghana are likely to be the only African representatives in the last 16.
Despite a large, vociferous backing in Soccer City in Johannesburg, Ghana were narrowly beaten by the Germans, who topped the group as a result.
"We played quite well, we resisted well, we had some chances but they had to win and they showed that they are among the best teams in the world," stated Rajevac.
"We knew it would be a tough match because Germany has an excellent team but we have qualified, that is the main thing."
Midfielder Mesut Ozil scored the only goal of an entertaining game in the 60th minute, but Ghana were not without their chances, most notably when Kwadwo Asamoah ran through prior to Ozil's goal, but could only shoot straight at keeper Manuel Neuer.
"It was a very difficult match but we fought and it was enough to get us through," said Ghana midfielder Andre Ayew. "We had opportunities but the important thing is that we went through."
The game was also notable for showcasing the first time two brothers had played each other in a World Cup match, with Ghana's Kevin-Prince Boateng lining up against sibling Jerome.
It was Kevin-Prince Boateng's foul in the FA Cup final that forced Germany captain Michael Ballack out of the tournament through injury but Rejevac did not feel his player was hampered by any extra pressure as a result of the incident, describing his performance as "fantastic".
"I thought the German players were extremely polite with him," added the Serbian coach.
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