In addition to what u/ehwilliams wrote, one would need to notice that the medieval military organization, whether similar to the retinues of the early medieval period or military service based on feudal benefices, more typical to high part of the aforementioned period, was more or less similar to the modern systems of reserves. Medieval armies were largely composed of landed nobility who were obliged to respond to the call of arms issue by their senior, alone or with specific number of adequately equipped combatants. These people were well-trained, had the entire equipment on hand and in theory were ready to leave for the rallying point at a moment's notice (in practice they had to organize the supplies, what took some time). And this form of organization was generally thought to be caused by the poor saturation of the market with readily available currency. In other words, local rulers had little money to pay for the upkeep of the troops but a lot of land they could have rented to potential soldiers in exchange of their loyalty. With the increase of currency and consolidation of central power, the popularity of knights relying on feudal obligations waned in favour of mercenaries and standing armies.

But there is one other important factor that explains alleged discrepancies between the size of Imperial Roman and Medieval European armies and this is the population size (the economical variables explain why Rome was able to maintain standing armies, unlike medieval states). The medieval armies seem small in comparison Roman ones mainly because the fragmentation of the polities that to some extent remained to this very day, as in modern Europe there is not a single country that would have encompassed half of the continent and the Northern Africa to boot (modern Russia somewhat qualifies territory-wise, but it still has a population equal to the next two largest countries; USSR would have been closer to the mark, but it does not exist anymore). In other words, Roman Empire was very, very large and populous in comparison with even the largest and most populous polities in the Middle Ages and Early Modern period.

Let's look at the numbers. Roman Empire, at its greater territorial extent under Traian and Hadrian (the first quarter of 2nd century CE) had an estimated population of 60 million people. European states in 14th-15th centuries were far smaller in comparison, with England being populated by less than 3 millions; Holy Roman Empire by roughly 10 millions; Spain by 6 millions, France, largest most populous of them all had 14 millions, and Poland with Lithuania (after the Union of Krewo in 1385) numbered slightly over 8 millions. So, it is clear that the entire Europe combined could have barely boasted a population of the Roman Empire in 2nd century. Now, during the reign of Hadrian, the number of the concurrently existing legions amounted to 31 what, assuming the nominal manpower of each one being roughly 5000-5500 soldiers gives us the total amount of 150.000-165.000 soldiers or 0.25% of the total population (in reality, this would have been somewhat smaller as legions were not always kept at full nominal strength). When we look at the estimated size of troops in the prominent battles of that period, we can see that there were up to 100.000 Roman soldiers taking part in the Siege of Sarmizegetusa in 106 CE (0.16%). Likewise, in the battle of Issos in 194 CE between Septimus Severus and Pescenius Niger the commanders fielded approximately 35.000 and 45.000 troops respectively what would amount to 0.058% and 0.075% of the total population of the Empire. This corresponds quite well to roughly 6.000 English troops at Azincourt in 1415 (0.2%) or 30.000 Polish and Lithuanian troops at the battle of Tannenberg in 1410 (0.33%), strongly suggesting that the perceived smaller size of medieval armies in comparison to ancient ones were caused primarily or even solely by the difference of population size. If we count in the remnants of the common defence under e.g. the fyrd system and the defence requirements of the people possessing full urban privileges, it would be possible to argue that the high-to-late medieval rulers could have actually counted on the larger forces relative to the population of their domains, than the Roman Emperors could have in the past.