The ending is deliberately somewhat ambiguous, because a lot of the movie deals with issues about reality/non-reality. I think you are supposed to decide for yourself whether you think she dies or not.
For a more concrete answer, I suggest that because Nina's life mirrors the Swan Lake story (ie White Swan VS Black Swan), then Nina does die at the end because that is how the White Swan's story ends.
Yes, she does because if you note the actual story of the Swan Queen, it's about a woman who turns into a swan, where a prince has fallen in love her. However, the woman falls for the wrong guy and kills herself. (Nina actually says something like this during the part of the film where she goes out clubbing). So, anyway, Nina falls for the wrong guy (her teacher, Thomas), who in the end calls her: "My little princess." Plus, with all the strain on her performing the role, she kills herself. Hence, why she says at the end: "I was perfect."
I'd recommend you maybe watch the film again and take note of where she goes face to face with Lily in her changing room, because that's one of most crucial parts related to the ending of the film. I hope this helped :)