First, lets compare Julius Caesar to some other tragedies written by Shakespeare - such as Romeo and Juliet, Hamlet, and Macbeth. In these three examples, the tragic character[s] of the plot are the title characters. However, in Julius Caesar, Brutus is the tragic character, the one who is brought down by his own failings and whose decisions affect the action of the play. The title character, Caesar, is a static character, experiencing no persoanl growth throughout his time in the story.
Also, in the three examples given, the title characters - being central to the play - are all killed off in the last act. Caesar is killed off in Act III, scene i. He is obviously not at the center of what the play is most concerned with.
The play, in fact, is not concerned with the life and death of this man. It is concerned with the motives and men behind his murder and the consequences of his murder. The characters at the center of this focus are Brutus, Cassius, and Marc Anthony. These are the dynamic characters, and the majority of the play follows their progress from initial idea, to murder, and through the aftermath. Caesar is only in three scenes, and thus is not the focus.