Yes, there is no point in counting India in Asia either through culture, geography, history or ethnicity.
India sits in its own continental plate and has a distinct culture. It has not ruled East Asia nor ruled by it. It is larger than Europe in population and it is plain Euro-centrism to see Europe as distinct from Asia [when they are a part of the same continental plate], but India as a part of Asia. India would satisfy every criteria to be a continent – large population [larger than other continents], separate continental plate, distinct cultural & linguistic groups and so on.
Source: NASA. The Indian Plate.
The Americans are often using the correct terminology by calling out the Asians, Indians and the Arabs distinctly [all of these are separate plates and separate cultural groups]. In UK, also this distinction is more common. I guess it is just a matter of being exposed to more of outside world.