The answer to this is actually quite simple. It didn't. Feudalism is a term used to describe a medieval system of land ownership that only came into being after the fall of the Roman Empire, including the notions of nobles as vassals of a king, and serfs as legally attached to the estates on which they lived. The Roman legal and economic system was quite different.
Roman law did not have serfs. People were divided into citizens of various classes, freedmen, and slaves. Free citizens and freedmen could own land; slaves and children still legally under patria potestas (the power of their fathers) could not own land but could have use of it through a legal device known as a peculiam. While freedmen had certain obligations to their former masters for two generations, after that they became citizens, with full rights of citizenship.
The closest Roman phenomenon to feudalism was latifundia, a system of extensive estates accumulated by members of the upper classes in the wake of conquests of foreign territories, but they were still not technically feudal in their organization.