The Serbs are being tipped as a potential surprise package having taken full advantage of France's troubles to top their qualifying group, and have high hopes of making it out of a tough Group D, where they will battle it out with Australia, Germany and Ghana.
But Chelsea's Ivanovic knows there is little margin for error with the stakes so high.
He told his club's official website: "We qualified in first position ahead of France, which was very good for us.
"We did a lot of good things and we have to continue to play like we did in the qualifiers.
"But of course, the World Cup is completely different to the qualifiers. If you make a mistake, it is very difficult.
"Every game is like a final in the World Cup and we have to remember this when we play."
Serbia face Poland in a warm-up game on Wednesday evening as they prepare for their first World Cup as a country in their own right.
Ivanovic said: "It is our first one as Serbia, and my first one. It is a pleasure and it makes me proud to play in a World Cup, as it is for any player.
"It is a special thing to play for your country and to represent them in a World Cup is the dream of every player. Every one of us is happy with this."