Romans did set a precedent, but probably not in the way you're thinking.

Generally speaking, Romans did not persecute Jews in the way that, say, medieval governments did. Rome did (harshly) put down a few Jewish rebellions. While they did occasionally restrict Jewish religious practice, this was far from the norm. In later periods, it was concieveable that a Jewish community minding its own business would be exiled or massacred or forcibly converted basically on a whim, whereas this would not have occurred under Roman rule.

What they did do is treat Jews as a group as a special legal category, which persisted into later times. Jews were able to use Jewish courts to adjudicate disputes between Jews with legally binding authority. While Jews could legally use non-Jewish courts, using a Jewish court would produce a legally enforceable judgement too, even if Jewish courts were somewhat restricted compared to non-Jewish ones (they could not execute from a fairly early date, and it was pretty common for them to only be able to deal with civil law and family law). Jews paid taxes in a different system that allowed them to live under Roman rule without participating in Roman civil religion.

As with a number of Roman institutions, this setup persisted after the Western Roman Empire formally fell. Jews as a community were governed by a different set of laws, one which allowed for a great deal of autonomy while still having some legal restrictions. Over time, these legal restrictions tended to become more and more stringent. But probably the most important change is that while this arrangement was quite stable under Rome, it could be quite unstable in Christian Medieval areas. Jewish community's special set of laws were governed by some sort of basic legal document, usually called a "charter". While in content these could be fairly similar to what you might find under Rome, the basic concept is that Jewish communities only existed under the protection of and by permission of the king. A change in monarch or a change in his opinions or other political machinations could make this legal arrangement evaporate entirely. This could make things very uncomfortable for Jews. A community could go from being normal residents of an area to being exiled with the stroke of a pen. And even beyond that, protection of Jews from phsyical violence relied on the monarch for protection from an unfriendly aristocracy (who often owed a few of the wealthier Jews money), unfriendly clergy (who often viewed Jews as a theological blight), and unfriendly other members of society (who might view Jews with suspicion as foreigners, as economic competition, or as a religious blight).

The basic Roman legal system with regard to the Jews, of a separate set of laws which allowed for communal autonomy with some legal restrictions did form the basis of later European models. But this basic model was altered in medieval times, and does not explain the whole of Jewish persecution in the post-Roman era.