First off, you should know that numbers for the size of armies are frequently suspect and embellished, although with that said, universally it's regarded that the Roman Empire fielded far more soldiers as a whole even within regions overlapping with later medieval kingdoms, than those kingdoms could muster up until the 15th or 16th century in western europe (eastern europe being another matter).

What changed was primarily the economic situation, as well as the nature of the threats to western medieval kingdoms.

The size of the Roman army was paid for by the economic wealth of the empire, which had the largest integrated economy the western world had known until the modern era. These troops were salaried and either stationed on the borders of the empire or attached to the emperor as a mobile strike force (during the late empire). Both type of armies being under quite persistent threat whether from civil war, foreign invasion or barbarian incursion, so their necessity was unquestioned, which is why an estimated half (possibly more) of all tax revenue generated by the empire went to its army.

Compare this to the medieval army, which was not a professional (salaried) standing army, but was a cadre of landed military aristocracy, who faced primarily "civil" threats amongst other aristocrats rather than existential ones, like outright invasion and conquest by a foreign state (though this would occur in the later middle ages).

This is in addition to the fact there simply wasn't the money to pay for an equivalent standing army, due to the breakdown of the Roman economy. The Roman economy was unique in the western world because of its equivalent of global trade and near universal taxation. It was dependent upon economies of scale, which once broken down, could not be reproduced in a local capacity that would makeup for the shortfall of the wider trade network.

Soldiers of the medieval era were generally not paid (well, except in booty). Military service could be seen as part of their obligations, official or unofficial, but it was a comparatively more adhoc affair when compared to a Roman army with its logistics trains of supply and recruit replacement.

And also, war is expensive. Which is why once you move out of late antiquity, military service was no longer in the form of a mass levy, where any male was liable for service. Since the economy couldn't support a standing army, only those who were rich enough to be in the army, were the army. Over time, that status codified into the military aristocracy we all know and love.

It's thus no coincidence that with the rise of centralized authority (and taxation) in the later middle ages, that the size of medieval armies increased correspondingly.

BTW, you can see the mirror of this outcome in eastern europe, where because the Byzantine Empire WAS facing existential threats from the Arab caliphate, they maintained an active standing army (believed to be the largest in europe), paid for by taxation (as this was how the Arab armies were paid as well). All aspects of the surviving eastern Roman Empire had to be mobilized in service to the state in order to survive, otherwise, they would've been taken over quite quickly by the Caliphates. And it also goes to show you, that even a relatively weak centralized state, was capable of extracting far more wealth to pay for a standing army, than the strongest landed polity.

tl;dr - Money and the nature of medieval threats vs. late antiquity threats