Kovac's men open their Group A campaign against the pre-tournament favourites at Arena Corinthians in Sao Paulo and face an uphill battle.
Brazil have not lost on home soil since 1975, when they were beaten 3-1 by Peru in Belo Horizonte in the Copa America, while the nation hosting the World Cup have never lost their opening game - with 14 wins and six draws in 20 previous matches.
However, Kovac is not daunted by the task at hand as Croatia attempt to spring a surprise against the overwhelming favourites.
"Everybody knows how much it means to us to play for Croatia," the 42-year-old told reporters.
"We will give our best in this historic match and I can assure that Croatians will be proud.
"We will try and surprise the hosts, and will not give up until the end. In the right circumstances, Croatia can make history."
Kovac added: "We are not going to park a bus tomorrow.
"We are going to attack and we are going to seek out chances, because Brazil is so strong that if you want to succeed against them, you have to score."
While Brazil boast stars such as Neymar, Oscar, Hulk, Fernandinho, and Ramires, Croatia are able to call upon a number of talented players themselves with Luka Modric, Ivan Rakitic, Ivan Perisic and Mateo Kovacic all at Kovac's disposal.
And Kovac bullishly suggested that the Brazilians may not be in for such an easy game: "We Croatians like to have possession of the ball, because if you have possession then your opponent cannot score. That's true isn't it?
"We also know that Brazil doesn't like to chase the ball too much. We will try to play possession football. Of course this will depend on both us and the opponent.
"We will try to keep the ball as long as possible. But also to create chances whenever we can.
"Of course it's easier said than done, we know that. But we will try to score and to try not to concede."
