There's an excellent book on the subject called
The Fall of Rome and the End of Civilization, by Bryan Ward-Perkins. It includes a detailed overview of the archeological evidence, which shows a very clear and dramatic decline in the economy and living standards -- and some areas of technology -- between circa 350 and 600 in the Western Empire. (And the recovery afterwards took centuries.) The
Eastern Empire, interestingly, doesn't show any signs of a similar decline until the 7th Century.
For example, peasant households in Italy at the height of the empire had a wide variety of well-made pottery, some of it originating from production centers hundreds of miles away, along with tiled roofs; after the collapse, the variety and quality of pottery was greatly reduced, and tiled roofs disappear. (Tiled roofs provide better protection against rain, are less flammable, and require less maintenance and rebuilding than wooden shingles or thatch; but they also require large kilns, lots of clay and fuel, and a good transportation network.)
And ice cores from Greenland show extensive metalworking going on in Western Europe (in the form of copper and lead pollution carried through the air) during the Roman Empire; after the collapse of the Western Empire, the pollution levels don't return to Roman-era values until the 16th Century.