Milan Jovanovic's 38th-minute strike and a second-half penalty save from keeper Vladimir Stojkovic were enough to see off the 10-man Germans, who had striker Miroslav Klose sent off before the break for a second bookable offence.
"This is a victory for our people, who for sure will know how to celebrate it," Antic said. "This team represents its people because it is energetic, it is ready to fight and to a certain extent, it is arrogant.
"What is certain is that Serbian people have recognised themselves in this team, so this is a victory dedicated to the Serbian people.''
But after Nemanja Vidic had needlessly handled inside the penalty area, Stojkovic dived to his left to keep out Lukas Podolski's spot-kick on the hour and ensure a first win over Germany since 1962, when Serbia was part of the former Yugoslavia.
Stojkovic, who joined Wigan on loan from Sporting Lisbon in January, said: "After so many years, to win against Germany at the World Cup, it is quite something, and I think we deserved it.
"As a group, we have worked so hard over the last two years and this is the end result of what we have achieved over those two years.''
Germany coach Joachim Low remained defiant in defeat as he turned his attention to Wednesday's decisive showdown with Ghana in Johannesburg.
"Of course we are disappointed now, we are devastated by this loss, but we have got the resolve and we have got the will to go through to the next round," Low said. "I don't think this is going to bog us down completely.''
"We had our difficulties getting into the game and did not control the pace the way, we had hoped for. In the second half, my team fought back and showed character."