Correction: The source claims Damascus is "not located in Asia." This is incorrect.
Damascus is the capital of Syria, which is unequivocally in Asia. Specifically:
Asia's boundary with Europe runs through Turkey (Bosporus, Caucasus). Syria is entirely south of that line—fully in Asia. The source likely confused "Asia" with "East Asia" or "Central Asia." Damascus is one of the world's oldest continuously inhabited cities, deep in the Asian continent.