When you picture the Roman Empire, you can imagine spectacular formations of fully armored legionnaires, beautiful cities with intricate government systems, and an absolutely monstrously large amount of territories. It is honestly difficult to believe that the barbaric and primitive tactics and systems of the Medieval Era came after the Roman Empire.
Why is there such a massive difference in the Roman Empire and the Kingdoms of post-Roman Europe? Was it due to the resources available? Is the Roman Empire merely extremely glorified and not at all how it is often portrayed? Are the Kingdoms in Europe after the fall of the Roman Empire much, much more advanced than we commonly imagine them to be?
(By fall, I'm referring to the 476 fall of the West Roman Empire, rather than the fall of the East Roman/Byzantine Empire in 1453.)
I don't know what kind of historical answer can be given to this. There could be the temptation to state the obvious that the Middle Ages were far from being "barbaric and primitive", because they weren't - that's a model of thinking about the medieval period that's been by and large abandoned, the more we learn about them and the more we lose our idolatrous fawning for Classical Antiquity.
Yet the problem here seems to be of a different order. You are surprised that something that came after could be worse than something that came before - and after giving the caveat of the previous paragraph, it's inescapable that the Roman State had at its disposal a number of technological comforts that eluded Western Europe for many centuries. That way of thinking is understandable, coming as we do from an idea of progress, that tells us that "History goes forwards", either technologically, with scientific progress making lives more comfortable, or else morally and from the point of view of civilization ("The arc of the moral universe is long, but it bends towards justice.")
We have little evidence to believe this to be true. It's likely to be and to remain one of the great questions of History, to be debated while there exists Humanity, and moreover who knows if the scientific revolution did not introduce into the equation elements that were previously absent. However, for all of observable history, we have nothing whatsoever to convince us that there is a historical rule that dictates that what comes before should be worse than what came after (or, for that matter, vice versa). For many reasons periods of prosperity and civilizational development are followed for periods of stagnation (if that's how we're going to judge). There may be many aspects at play here to influence the flow of prosperity, but "chronological order" it seems was not one of them.
So much for what I understood to be the underlying spirit of your question. The more concrete question, which we could perhaps rephrase as "what happened to the Roman Empire?" - well, it's a question people of every kind and sort have been trying to answer ever since it fell. The question of the "Decline and Fall of the Roman Empire" has been on the minds of Western Europe ever since Augustine wrote his City of God. There isn't one answer, and besides this sub is full of answers to more specific variants of that question: a combination of a collapse of centralized authority and technical expertise, the dismantling of taxation, a return to a goods (rather than a coin-based) economy, wars, migrations, and invasions, as well as many other reasons, are probably to account for why the Roman Empire ended.
The Medieval states lacked both the resources, the will, and maybe even the ideology to reconstruct it. Some of the technology had been lost, some was available but was no longer interesting because the priorities had changed - you settle into a patch of land that's well-watered so you don't have to build aqueducts, for instance.
While all of this is happening, the Islamic Caliphates at first, and later the Roman Empire to the East (Byzantium) were going at very enviable paces, which the Roman State of the Classical Period would have very much liked to have immitated.
I think I can answer this having studied art history.
It wasn't so much that the Romans were more advanced than people in the medieval era, it was that they were more organized. The splintering of the Roman empire into smaller principalities led to corruption and disorganization. So, much of society would not benefit. In reality in many ways society was far more advanced technologically.
The problem was that you would not really experience better technology unless you were wealthy. You also have to consider that in many ways areas of the Northern parts of Europe were less settled. This would be similar to having log cabins in America vs having castles in Europe. Civilizations are built with provisional structures before better more permanent structures are built.
We also have to take into account population increases and decreases. Many times during the era Europe would be over-populated. Then there would be plagues and society would collapse. Paris was an ancient city, but it had issues with having more people than it could handle. At many times walking through the city you could encounter toxic chemicals. Certain places might be better in one era and be terrible in another era.
It may seem like Rome was a better place to live, but in many ways it would not be a great place to live. While the society was really good at public works projects, and had some semblance of democracy, it also had slavery and was at constant war.
To make a comparison to the last century: In the late 60s and early 70s people walked on the moon. It's been about 46 years. While, that is impressive and it seems like we're back on track, we have to keep in mind we have amazing computer technology now. People in the future might look at the last 46 years and wonder "what happened?" It might be very hard to grasp the importance to a lot of changes our society has gone through during the interim.
At least in the one area where I think I have some genuine expertise, the history of agriculture, the "Dark Ages" were a period of major technological change. The Romans used a two field agriculture system. That is, they would plant crops year one year and leave it fallow for the next to recharge nutrients. You saw a move to a three field system usually with wheat one year, a nitrogen fixing crop like peas the second, and fallow the third. You also saw the move away from scratch ploughs (a plough that was made of wood with a metal tip) to ploughs with much more metal and with a muldboard design that's a sort of turnup that will dig up nutrients deeper in the soil. These technological developments required new types of harnesses for the horse, and improved horse breeding in general. Records from the period are scanty, but we also saw a massive increase in the use of wind and watermills during the period between the fall of the Roman Empire and the Carolignian period. Given that the overwhelming majority of people lived in rural areas and were farmers, the effect of the agricultural revolution of the middle ages are hard to overstate.
EDIT: I earlier asked why agricultural technology saw such massive increases during a period that would otherwise seem so unconducive to technological change. I would be really interested if anyone has any answers here.