Okay, so "civilize" may not be the best work here. When the Romans moved into the Balkans the Illyrians were actually a rather powerful regional power. In the illyrian wars they just found themselves fighting a much stronger foe, the much more centralized Romans. The Balkans were eventually Incorporated into the empire and although it wasn't the most valuable province, it was certainly not an irrelevant backwoods. In fact, the provinces that made up the Balkans were generally significantly more stable and prosperous than other provinces. Many prominent Romans came from what is now the Balkans, including several emperors. When the empire split, the Balkans were of course Incorporated into the eastern empire. Once again the Balkans became a very reliable source of men and money for the eastern empire. Starting around the same time as the decline of the western empire, several barbarian incursions affected the Balkans, first consentual immigration and later more violent invasions. It is in this period that the Balkans prosperity began to decline, although the several fortified cities along the Adriatic coast became sanctuaries of trade and culture, ie: Dubrovnik, (who would go on to become a major trading rival to the republic of Venice). As the eastern Roman borders receded south over time, Roman influence and culture left with it.