The Vatreni head coach insists he won't let the ongoing controversy affect his side, as he looks to delay his departure with a victory over Spain to book a quarter-final place
A banana was allegedly thrown in the direction of Azzurri striker Mario Balotelli, while chants and banners of a discriminatory nature were on display between the two sides on Thursday.
Speaking at a press conference ahead of Monday's match with Spain, Bilic fumed: "Look, of course, this is my personal opinion and this is what we talk with the players.
"It is a big problem all around Europe and all around the world and on behalf of the whole Croatian nation I am really disappointed as a Croatian, as a parent, as a sportsman and a person who comes from a modern, open minded and tolerant state."
However, Bilic is adamant only a small contingent of the Croatian support had partaken in such activity, adding: "Everyone is welcome in our country, I don’t like these kind of supporters and nor do my players.
"I live in Croatia. We are a really a tolerant country, not a racist one and we are angry at these few crazy supporters. We have to lay down sanctions and try to stop these kind of supporters for good."
The 43-year-old will become the next coach of Lokomotiv Moscow after Croatia's Euro 2012 campaign, but Bilic believes he has unfinished business with the national team, starting with a win over reigning champions Spain.
"I'm convinced that this is not going to be my last match, but if that happens, I'll leave the team assured that we did a great job," he stated.
"Whatever happens, we will finish these championships with our heads held high and proud of what we accomplished.
"I expect us to play the best possible match against Spain and a repeat performance of the ones we produced against England in Zagreb, Germany in Klagenfurt and Turkey in Istanbul."
Looking ahead to the match itself, Bilic insists he will not adopt a more defensive approach against La Roja, as he wants to see his side hold their own against such a talented outfit and make their possession of the ball count.
"We'll do our best to avoid [playing defensively], but Spain make their opponents do that with their possession of the ball, and they will do the same against us.
"However, teams [who deploy systems to counter them] have produced good results in the past, like Switzerland or Chelsea. To achieve our goals, we must simply want to win more than them.
"They will not underestimate us, that is for sure, and they are the best team in the world. Still, they are not Barcelona.
"Torres has a huge impact on this team and I would prefer if he stays sidelined, but I'm convinced that he will play.
"It is very important to interrupt their rhythm, and take the ball from time to time. That makes them nervous and, at the same time, allows our defence to rest.
"We are physically and psychologically ready, and confident that we can go through. We want to see Ukraine!"
Asked whether he could expect help from Republic of Ireland, who face Italy in the final group fixture, Bilic was in no doubt, stating: "I think they can, they are that kind of nation - a proud one - and it's not the same for them to go home with or without points."