A win would have steered Serbia into next year's finals and they looked to be on their way after Nenad Milijas gave them the lead with a soft penalty, which also produced a red card for France goalkeeper Hugo Lloris.
Thierry Henry equalised in the 31st minute and France dominated proceedings in the second half, laying siege to the Serbian goal in the closing stages.
"France showed great morale and determination after falling behind, they kept possession really well and in the end we had to settle for a draw," Antic told a news conference.
"It was an extremely demanding game for us physically, mentally and tactically because it did not show that France were a man down after nine minutes.
"We had a great chance to secure our World Cup berth tonight but the opportunity also put a lot of pressure on our shoulders and I think my players dealt with it well.
"I am confident that we will finish the job when we play Romania here next month and I also hope for another full house in Red Star's stadium."
France coach Raymond Domenech, under pressure after a patchy qualifying campaign in which the 2006 finalists are still not assured of even a play-off berth, was delighted with his team's performance.
"It was an exceptional match and that's the way we want to see the team play, with enthusiasm and quality," he told the French TF1 television station after the match.
"I am happy we could show this to all those in France who keep supporting us," he added.
France playmaker Yoann Gourcuff said: "To concede an early goal and find ourselves down to 10 men after a few minutes was very tough mentally but we kept fighting and displayed an irreproachable spirit.
"In such conditions a draw is not a bad result but I really believe we would have won the match had we stayed with 11 men."
