Willy Loman in Death of a Salesman by Arthur Miller does not fit the classical model of a tragic hero. In classical tragedy, the hero was always a figure larger than life. He typically had noble parents, and often had some divine blood. The hero was normally a powerful or honored member of the community, often a king or an outstanding warrior. What made a play a tragedy was that it focused on the fall of someone admirable, who might have been victim of a curse or possessed of a tragic flaw.
Willy Loman is none of these things. He is a middle class salesman, rather than a noble or ruler, and not even particularly good at his job. There is no sense of the gods being concerned with his fate; this is a purely secular drama. Instead, rather than a tragedy in the classical mode, this is a modern drama with a protagonist who is almost an anti-hero.