During Croatia's 2-2 draw with Albania on Wednesday, both sets of supporters were accused of singing offensive chants towards Serbia, which has left the country's FA furious and demanding punishments.
UEFA are yet to confirm whether action will be taken against either football association, though Serbia are confident that the governing body will bring sanctions towards their fellow competitors or they will "not continue" in Germany.
"What happened is scandalous and we will ask UEFA for sanctions, even at the cost of not continuing the competition," Serbian FA General Secretary Jovan Surbatovic said.
"We are sure that they will be punished, because they have already responded to our appeal to remove the so-called journalist from Albania from the championship. We will request UEFA to punish the federations of both selections. We don't want to participate in that, but if UEFA doesn't punish them, we will think about how to proceed.
"We were punished for the cases of fishing and our fans behaved much better than the others. One fan was fined for racist abuse and we don't want it to be attributed to others. We Serbs are gentlemen and we have an open heart, so I appeal to the fans to remain gentlemen."
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Albania celebrating with their fans after scoring against Croatia. (Image: Getty)
If UEFA decide against punishing Croatia and Albania, and Serbia follow through with their threat to quit the competition, it would leave a group consisting of England, Denmark and Slovenia in chaos.
Serbia are due to play Slovenia at 2.00pm on Thursday, with their final Group C match with Denmark scheduled for Tuesday.
According to UEFA laws, Denmark and/or Slovenia would be handed an automatic 3-0 win if Serbia pull out of the competition, with the FA set to land a big fine.
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Albania were also fined for actions in their 2-1 defeat to Italy for the "lighting of fireworks", "throwing of objects", a "pitch invasion" and "transmitting provocative messages not fit for a sports event".