The Serbians, who top Europe's Group Seven with 19 points from eight matches, need one win from their final two qualifiers - at home to Romania on Saturday or away to Lithuania the following Wednesday - to book a place in next year's finals.
"We have a great chance, we have earned it because we have worked hard to be in this position and we now need to make the final step towards South Africa," Antic told Reuters.
"I know what the national team and its success means to people in Serbia, we are flattered by the attention we are getting but now is crunch time and I will do everything in my power to make sure we seize the opportunity.
"Many of our players are in good form for their clubs and that's another reason we are optimistic that we can finish the job in Belgrade against the Romanians."
Antic, who took over in 2008 from Miroslav Djukic only two weeks before the World Cup qualifiers began, said steering Serbia to the finals would emulate winning the Spanish league and cup double with Atletico Madrid in 1996.
"You can't really compare the two achievements but I am in a privileged position to be on the brink of taking Serbia to the World Cup finals for the first time as an independent nation and the accomplishment would give me as much joy.
"I am sure the players will be getting more anxious as the Romania match draws closer and we really can't wait for it."
FRESH BLOOD
Serbia and Montenegro played as a single country at the 2006 World Cup in Germany and their ageing team made an early exit after three defeats in as many group matches.
Serbia then failed to qualify for Euro 2008 under Spaniard Javier Clemente and his successor Djukic endured a brief and unsuccessful spell afterwards.
Antic injected fresh blood into the team and it paid dividends as Serbia produced a string of impressive performances in the World Cup qualifiers, with left back Ivan Obradovic one of those who made an immediate impact.
Obradovic scored in his third international appearance in a 3-1 win in Austria and is confident Serbia will fulfil his childhood dream of playing in the World Cup.
"It is every player's dream to be in the World Cup and if you can fulfil it at the age of 21 there aren't too many things left to be desired, it's the best thing that could happen to me in my young career," he said.
"We are completely convinced that we will celebrate qualification on Saturday and we will come at Romania with full force, but we must not throw caution to the wind because they are a good team."
