I think you’re underestimating the sophistication of medieval societies. See this r/askhistorians thread about how the view of medieval society as barbaric is largely discarded at this point.

As far as your specific question, the Romans considered naval pursuits to be of less importance and less worthy of glory than land-based combat. David Potter in “The Roman Army and Navy” goes so far as to describe naval pursuits as un-Roman. As such, I’d say it’s unlikely that the Romans would have a lost-to-time naval advancement. However, I’d be happy to be proven wrong.

On the Greek side, the Eastern Romans invented Greek Fire sometime in the 7th century.

I think I should point out something extremely important here: while in the popular imagination and among 19th century thinkers the Romans are thought of as technologically more advanced than their medieval counterparts, the orthodox opinion of scholars has been, since about 1920, precisely the opposite. The orthodox position is that the Greek and Roman world was technologically stagnant, and that the Middle Ages were a period of massive and rapid technological growth, albeit mainly in areas like agriculture and shipbuilding that are not as glamorous as the monumental architecture of the Romans (which was nevertheless rivaled later in the period). I've talked about this here: only since about the 1980s have ancient historians seriously begun to consider the possibility that the Roman world might have had even a concept of technological progress. The popular perception is a cultural one, and does not actually represent the scholarly consensus (or, as it is at the moment, the lack of consensus).

It should also be noted that much of Medieval shipbuilding not only built on top of Roman technology, but blended in the best elements of Norse shipbuilding traditions as well (and Northern European shipbuilding had to contend with generally more hostile conditions than the Roman Mediterranean; as early as Caesar's invasions of Britain it was noted that ramming just plain did not work on Gallic ships in the channel, since they were more sturdily built than what the Romans were used to). That, plus the development of things like skeleton-first construction, clinker construction, and (as time goes on) more complex rigging systems, meant that typical Medieval cogs and other such "round ships" were technologically well beyond what the Romans put in the water.

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NAM Rodgers, The Safeguard of the Sea, "Ships" chapters
Lincoln Paine, The Sea and Civilization
Charles Stanton, Medieval Maritime Warfare