By definition, tragic means something melancholy, mournful, pathetic, dreadful, and/or disastrous. That being said, while William Shakespeare's play does depict the deaths of both protagonists, Romeo and Juliet, the plays tragedy extends far past their deaths.
For readers, or viewers of the play, Romeo and Juliet is tragic because of the feelings associated with the action of the play. The fact that these "star-cross'd lovers" die in the end is not the only tragedy. Even more so, the story of the long feud between the Montagues and Capulets is tragic. The fact that many deaths have come from the families fighting proves the play to be tragic as well.
Many tragedies evoke feelings of sadness from its viewers. The fact that the audience, reader or viewer, follows along the doomed couple proves to be one of the most tragic things which happens in the play. While the sadness ends for both Romeo and Juliet at the close of the curtain, readers/viewers must leave feeling the heaviness of a doomed love lurking.
Those questioning the tragedy of the play must remember that Romeo and Juliet are not the only characters who die. Mercutio, Paris, Tybalt and Lady Montague also die. The numbers of death alone make the play tragic.