Elizabethan tragedy had several key tenets which can be observed in all of Shakespeare's best tragic works. To begin with, a tragedy always had to end in disaster, in practice almost always a death. This should certainly include the death of the main or eponymous character, but in Shakespeare's plays, it often encompasses many other characters as well. Consider Othello, which ends in a literal pile of bodies (Othello, Desdemona, Emilia, and Roderigo all die).
Importantly, this tragedy must also come about as a result of the hero's hubris, or fatal flaw. That is, there must be some element of the hero's character that leads to his downfall, his own death and that of whoever else is caught up in the play's tragic events. Othello's fatal flaw is typically held to be his jealousy, which enabled Iago to manipulate him so easily into believing Desdemona was unfaithful to him.
Despite this flaw, however, the main character in an Elizabethan drama must be somebody sympathetic in the eyes of the audience. If an obviously evil man causes his own downfall through flaws in his character, the play will not be a good tragedy. The reason the flaw is a fatal flaw is that the lead character in a tragedy must otherwise be a good person, whose Achilles heel allows him to be corrupted. We see this in Othello, who is an upstanding and respected soldier; Macbeth is a loyal nobleman corrupted by his desire for power and his weakness in the face of his wife; Hamlet is an honest prince driven to madness by his thirst for revenge. It is because of this tenet of Elizabethan tragedy that Othello cannot be called Iago, even though Iago arguably has a bigger and more important part. It is the tragedy of Othello because it is Othello who suffers, and Othello is the good man brought down by his tragic weakness.