Been reading a long paper about the fall of Rome recently. Might add some stuff.
Indeed people at the time didn't see 476 as something of importance, compared to what happened in 410 (sack of Rome by the Wisigoths). This to say that empires don't fall in one day (this sack lasted 3 days

), but it is a continuous process.
Some think that Antiquity had reached her limits, and that something new had to be injected so as to start a new era. The Germanic Barbarians were given that role. With the definitive break between the West and the East in 395, the proto-European sphere starts to emerge. The Barbarians were the key for that Europe to evolve and conquer the world 1,000 years later. Of course they didn't do it on purpose.

But the fall of Rome helped the European cause. The irony is that it's Constantinople which "sent" some barbarians to the West in the 5th century, and will later be sacked by... the European crusaders. Constantinople... still living mostly on her Greco-Roman heritage.
It's also said that the fall of Rome isn't to be taken as a "better" or a "worse", it was just the beginning of a slow evolution to the next level. Antiquity seemed to be staggering ; is that what Decadence is about ?
Finally, the paper cites an Italian dude who talks about "the noiseless fall of an empire in 476". Which brings 2 facts :
- it is the fall of an empire, the person of the emperor (the most important figure) disappearing, which will definitively allow the Barbarians to organize "Europe" as they wish [476 is an important date and had serious consequences] ;
- it was hardly spot by people back then, because this wasn't the first sign of a dying empire, and some may have thought that this was just yet another temporary step down ? [476 isn't that important itself, other dates have significant importance]