You can argue there was still an Eastern Roman Empire. You can point out that a part of France (The Domain of Soissons) remained Roman for another decade. You can note that Eastern Romans actually managed to recapture Rome in 540.
But, really, in 476 it was over.
There used to be this theory that vast numbers of barbarians overran the place. Subsequent archaeological research revealed "IT" continued to putt along until 535 ~ that's the year even China turned to poop.