A continent can be both geographical and socio-historical (and indeed, both simultaneously). Technically mainland Europe, Asia and Africa are one gigantic landmass and should be treated as one continent if we stick to the 'separated by an ocean' rule, but this ignores the fact that continents are also communities of nations centered around a particular area of land. In this latter sense, Europe and Asia are two distinct continents but only because we subjectively recognise them as such.
tl;dr: Culturally and historically, Europe is a continent. Geographically, it's a more murky picture but that doesn't mean that we're 'in Asia'.