Wikipedia agrees but I am certainly no expert in this:
The "Dark Ages" is a historical periodization traditionally referring to the Early Middle Ages or Middle Ages, that asserts that a demographic, cultural, and economic deterioration occurred in Western Europe following the decline of the Roman Empire.[1][2]
Petrarch, who conceived the idea of a European "Dark Age". From Cycle of Famous Men and Women, Andrea di Bartolo di Bargilla, c. 1450 The term employs traditional light-versus-darkness imagery to contrast the era's "darkness" (lack of records) with earlier and later periods of "light" (abundance of records).
Petrarch, the 14th C dude you're referencing, believed in a two age history demarcated by the fall of Rome and that he was living in dark, post-Roman world. The three age history of light-dark-light that would give us the term middle ages/medieval wouldn't come til the 15th C with Bruni when he tacked a modern age onto Petrarch's scheme.
The Dark Ages are from ~500AD to ~900AD and as a term were first used in the 14th century. I don't know how else you would describe a period in which population was reduced to less than a quarter of what it had been at the peak of the Pax Romana.