They did not speak. This was disappointing, for Miss Brill always looked forward to the conversation. She had become really quite expert, she thought, at listening as though she didn't listen, at sitting in other people's lives just for a minute while they talked round her.
A significant quote showing Miss Brill's loneliness is seen above. It describes for us how Miss Brill conducts her conversations: she is on the fringe and only listening in while pretending to be keeping to herself. In order for Miss Brill to even have a chance at not being lonely, she would need to engage in active conversation with the other concert attendees. The fact that she keeps isolated yet eavesdrops delicately ("She had become really quite expert, ... at listening as though she didn't listen ...") indicates her loneliness.
It must be acknowledged, though, that Miss Brill doesn't deeply feel this loneliness because of the turn of her disposition and the traits of her personality. This natural or deeply bred tendency is illustrated in her pleasure and thoughts while listening to the concert:
Now there came a little "flutey" bit--very pretty!--a little chain of bright drops. She was sure it would be repeated. It was; she lifted her head and smiled.
Nonetheless, she does feel slight stirrings caused by her loneliness, although she seems unable to identify the nature of these stirrings:
And when she breathed, something light and sad--no, not sad, exactly--something gentle seemed to move in her bosom.