I'm not quite sure how to answer this, as I have always thought that 'Roman-ness' was widespread and endured long after the fall of the Western Roman Empire. By late antiquity, people from Egypt to Britannia generally thought of themselves as Romans, even though ethnically and linguistically they were very different. From my perspective, their Roman identity was already more than an affiliation with a single city, but an imperial identity that included a huge range of peoples - there was no need for a broader Italian identity, as their identity as citizens of the Roman Empire was broad enough already. Even when Rome the city was no longer important (as it was eclipsed by Trier, Ravenna, Constantinople, Milan etc), after centuries of dominance by Rome the concept of Roman-ness meant so much more than just being associated with the capital city of the empire, but one associated with the empire as a whole.

This association continued long after 476. In the sixth century for example legal distinctions between Romans and their Germanic rulers are visible in all western law-codes of this time, even though imperial authority had disappeared. This is particularly obvious in southern Gaul, where Franks and Visigoths only ruled loosely as overlords, allowing Roman-ness to flourish. This was not a Roman world associated with Rome the city or to Italy, but a world dominated by an ethnic and cultural identity linked to their history within the empire. In the east it is even more obvious, as people identified themselves as Romans even after the fall of Constantinople in 1453. The Roman Empire was not just the empire of a single city, nor of the Italian Peninsula, but an entity that incorporated many different concepts within itself, to the extent that Rome no longer meant just Rome - why else would the Holy Roman Empire, the Ottomans and the Russians all want to associate themselves with it?