Tennessee Williams's classic play The Glass Menagerie is a tragedy because each member of the Wingfield family suffers in their own individual way and Amanda's plan for Jim O'Connor to court her handicapped daughter ends in disaster. Williams creates a somber atmosphere throughout the play as each member of the Wingfield family struggles with the burden of their unfulfilled dreams. Amanda Wingfield is overwhelmed with loneliness, instability, and uncertainty after her husband abandoned her and relies on her son to financially provide for the family. Instead of facing reality, she escapes to memories of her past and harbors unrealistic dreams for Laura. Amanda's plan for Jim O'Connor to be with Laura is shattered after it is revealed that he is married. Amanda's constant nagging and demanding nature also cause her son to abandon the family. Following Jim O'Connor's visit, Laura retreats back to the imaginary world of her "glass menagerie" and Tom is haunted by the memory of his fragile sister. Despite attaining independence, Tom is plagued by his decision to abandon his family and cannot overcome the difficult memory. Overall, the memory play has a tragic ending, where each member of the Wingfield family is emotionally scarred and does not attain their dreams.

"The Glass Menagerie" is a tragedy because the Wingfields are all living with disappointment, loneliness and a sense of abandonment. 

Amanda abandoned by her husband, struggles with her loneliness and barely keeps her disappointment contained.  The crushing blow, of course, is the news that Jim is engaged and that Tom did not know it.  Amanda's expectations are never met in this play.  She is constantly turned away, first when she tries to sell magazine subscriptions on the telephone, then by her son, who can't understand his demanding, controlling mother beyond her obvious displays of a past that is probably exaggerated.  Tom and Amanda never really communicate.  There is no real sense of family between the Wingfields.  They are hollow, just going through the motions of being a family.

Amanda is so lonely, more so than Tom or Laura, because they have each other.  Tom and Laura are both dreamers not doers. Amanda is locked in the past, the only place where she is welcome.

The end of this play is also tragic, not because someone dies, but because it signals the death of a relationship, between Tom and Laura.  Tom is then set adrift in the world of his choosing, haunted by the memory of his sister.  

Dictionary.com defines tragedy as "a dramatic composition, often in verse, dealing with a serious or somber theme, typically that of a great person destined through a flaw of character or conflict with some overpowering force, as fate or society, to downfall or destruction" ("Tragedy").  In The Glass Menagerie, we definitely have somber themes and serious themes of family strife, resentment, anger, etc.  There is clearly dysfunction in this family and Tom has been held back from being able to do the things he wants to do because of his feelings of being obligated to support his family since he is the only male.  Although he is able to "escape" the oppressive environment that he has lived in with Amanda and Laura, he doesn't really seemed destined for greatness.  He has only been able to distance himself from them, but he still feels guilty about leaving Laura, his sister.  He will not forget this:

When he functions as narrator at a time several years after the action of the play, readers understand that he has escaped physically but not emotionally. (eNotes)