Cacic's men were winning 2-1 against the Czech Republic in Saint-Etienne when a series of flares were thrown onto the pitch from the Croatia end at Stade Geoffroy-Guichard.
One member of stadium security fell and had to be helped off the field after an object exploded next to him while attempting to clear the playing surface.
Several Croatia players pleaded with their fans to stop the disruption, which prompted an angry confrontation between their supporters as riot police watched on and stewards attempted to intervene.
The delay appeared to affect Cacic's players, who conceded a late penalty to draw 2-2 after dominating throughout.
The incident, which also saw a banner displayed in the stands, is believed to have been a premeditated demonstration aimed at Croatia's Football Federation [HNS].
And afterwards Cacic issued a damning condemnation of the actions of what he described as a shameful minority.
"I hope this will never happen again in the tournament," he said.
"It was like terror. They are hooligans, not supporters. Their place is not in the stadiums.
"The same happened in Milan against Italy. Even part of the Croatian media was not happy with my comments about that. We saw some Nazi signs on the Hajduk pitch against Poland. They ruin everything we are doing. Probably they have some support from somewhere but 90 percent of Croatian supporters are shamed in front of the whole of Europe.
"This is about six, seven individuals. I hope we can identify them and punish then, I hope the FA is doing everything to prevent it but it's impossible to avoid. These people are very scary. We knew there were threats. I am sorry. These are not real Croatian supporters. They are sports terrorists. We have so much experience with that. It hurts so much.
"[The] Croatian FA cannot fight alone against these hooligans."
UEFA have confirmed they will investigate the incident and Croatia may now face similar sanctions to Russia, who received a suspended disqualification after trouble against England at Stade Velodrome in Marseille.