That's a common read, but when you did into technological archeology, its not true. They didn't get a country that had the reach Rome did, and there were selective areas where Rome had an edge (we just figured out what they were doing with their form of concrete in the last few years), but the overall technological level of Europe had caught back up by about the sixth century.
And frankly, for long periods prior to that, I would describe some parts of Europe as post-apocalyptic. The only reason the rest weren't was that those parts didn't really fall in the first place. Rome just withdrew, but the regions still kept going under local leadership. Its more analogous to a situation where, say, the U.S. fragmented into separate nations. The not only didn't really fall, a lot of them never stopped trading with other nations in the first place.
What you lacked for a long time was anyone in serious expansionist-mode, but that's not a necessity.