Asia was the Greek name for the region to the east of the Aegean sea. For the Romans it referred to a specific province of the empire with its capital at Pergamos. Etymologically it probably derives from the Semetic root "Asu" meaning "to rise", I.E. EXACTLY THE SAME AS THE WORD "ORIENT", just from a Semetic rather than Latin root.

So if you are offended by the word Orient because of its Eurocentric origin, than Asia is just as offensive. In fact more so, because at least Orient was always a general term for the east, whereas Asia was a specific term that referred exclusively to a small portion of modern day Turkey, that happened to be immediately to the east of the easternmost Ionian Greek city states. It's the equivalent of naming North America "Manhattan" because that's the first place you reach if you go west from Long Island.

Of course, the origin of the words is unimportant. What matters is that TODAY the Orient refers to China-Korea-Japan, and Asia to the entire continent. So to use the latter as an adjective when you mean *only* the former is not only unnecessarily confusing but just straight up wrong. If you do wish to include absolutely the whole continent, "Asian" is fine, but so broad a term that it becomes meaningless. Might as well describe something as "earthly".

Terms I think are specific enough to add useful meaning as an adjective:

Middle Eastern (Arab countries east of Lybia, Israel, Turkey, Iran)
Causasian (former Soviet republics in the Caucasus mountains)
Central Asian ("-istan" former Soviet republics + Afghanistan)
South Asian (all countries in SAARC)
South East Asian (all countries in ASEAN)
East Asian (China, Korea, Japan, Mongolia)

I consider some countries as belonging to more than one of these(eg Vietnam is both East & S.E. Asian) and some countries include provinces that belong to a different region than the country as a whole (eg Xinjiang province in China is Central Asian), but overall that list seems pretty straightforward.

I myself am Indonesian, and would prefer to be called South East Asian. In fact I would probably correct someone calling me "Asian".