The technique used by these DNA analysis sites cannot be precise about your ancestry because they fundamentally work backward to the conclusions they draw of your background. 23andMe uses genotyping to give you results about your ancestry and health. What this means in simple terms is that your DNA is analysed at specific locations throughout the genome, and the genetic variant at each location is used to draw conclusions about ancestry. Accuracy is achieved by sampling thousands of different locations. The conclusions drawn are contingent on a comparison of your genotype compared to a data bank of genotypes that these companies have compiled of populations around the world. For example, your % of Italian-ness is determined by comparing the similarities of your genotypic results to that of modern Italians in the data bank. This is why it is impossible to draw conclusions about ancestral conclusions beyond that of extant populations. Most modern Italians are probably a mix of Italic native peoples, germanic migrants, and Celtic peoples and so you can only be compared to that data set. In order to draw conclusions about ancient or even early medieval ancestry, you would have to have a data bank of ancient genotypes to compare to. This would be near impossible to compile as there simply arent enough complete genetic samples to create this from. Any DNA test which claims to tell you about your ancestry in relation to distinct ancient populations is trash basically.

I would also suggest that, while you read the history of the world, remembering that the Romans controlled much of Europe for near 500 years they almost never supplanted native populations. At the collapse of the roman empire the people living in Gaul, though bearing little resemblance culturally to their ancestors of 200 BCE, were genealogically, likely unchanged aside from maybe some noble families. Even during the migration period in the "dark ages" when germanic tribes were displaced and settled all over Europe, their effect on the gene pool of the populations was not as marked as you might think. For example, to use my country as an example, Saxons, Angles, Frisians, and Jutes settled in England from the end of the 4th century onward, the Romano British; that is to say primarily Brittonic peoples whose society was headed by a mixed Roman and native aristocracy, were swept aside by hordes of Saxons who settled and took to the lands themselves leaving only the west (Wales and Cornwall) and the north (Strathclyde and the Highlands) to the natives. That's how the story goes at least. Though a recent genome sequencing study (a much more thorough analytic technique compared to genotyping) compared the genomes of 10 bodies found in Saxon burials in the southeast of England to modern South easterners in England. Turned out the average English man is only about 38% Anglo-Saxon. When the normans Invaded in 1066 they brought much cultural change but only about 5000-10,000 settlers, who took positions in the upper echelons of society, a drop in the ocean compared to the "Anglo-Saxon" population. I don't have the numbers but I imagine similar patterns emerge when you look at the birth of any new kingdom and the apparent destruction of the old one.

I rambled there but I hope I answered your question, basically, if 23 and Me say you are Italian you are probably a mix of Latin, Gallic, Lombard, Greek, Goth, probably many more, just like other modern Italians are. Right now there are no commercially available techniques to tell otherwise. :)