Tragedy, a very Western term (from Aristotle) requires all kinds of criteria: a great figure must fall from a great height, and there must be a "catharsis" (a cleansing) for the viewers or readers; Eastern philosophies, in my limited understanding, concentrate on Karma, Fate, and getting in tune with the All. Human actions are "dharma" (illusion), so you should apply these criteria to Karna's fate. "Tragic" is not a synonym for "sad"; it is a specific genre, reserved for stories of human striving, hubris (overweening pride), and other human actions, seen as "tragic" by an audience. It would be valuable to determine an Eastern vocabulary to describe Karna's story; of course, it proceeds on a symbolic level as well as narrative level.
Tragedy played very important part in the life of karna because his mother left him alone and then, when he came back as a mature man he was killed by his own brother, and what a great coincident the God who was present there he know everything and be a part of his killing.