I must admit, I think the ending of this excellent short story is rather unequivocal. Let us remember that we are presented with a woman who is profoundly lacking in self-awareness, as her fantasy of the huge drama at the park shows, in which even she is given a part and therefore importance. We are presented with a female character who does everything she can to distract herself from her own insignificance and lack of relations. She is overtly blind to this, but what is key about the final paragraph of this tale is the way that at least part of her recognises the truth of her own insignificance:
But today she passed the bakey's by, climbed the stairs, went into the little dark room--her room like a cupboard--and sat down on the red eiderdown. She sat there for a long time. The box that the fur came out of was on the bed. She unclasped the necklet quickly; quickly, without looking, laid it inside. But when she put the lid on she thought she heard something crying.
Key phrases to focus on are the way which the room is described as being "like a cupboard," just as Miss Brill, at the beginning of the story, looks at other people and imagines them to live in rooms like cupboards as well. Also, note her response to her necklet that she took such pride in at the beginning of the tale. She, at some level, is humiliated, embarrassed and ashamed at what she overheard the young couple say about her as it resonates deeply within her and makes her realise just how ridiculous and lonely she is. The crying at the end of the story is therefore the sound of her own sobs.