Yes, the narrator has his realization or epiphany when he overhears a conversation in one of the stalls and then converses with the young lady selling souvenirs. Prior to this moment, the narrator had built Mangan's sister up into a divine creature and he, naive as he was, set out to find an exotic prize from the bazaar. The bazaar is called "Araby." The "Arab" connotation implies something exotic for the narrator, something from a far away land; the Middle East. The narrator gets excited that he will be off on a sort of quest to bring something back to Mangan's sister; as if he is off to find a Holy Grail to bring back to his queen. When he overhears the pointless conversation between the people at the bazaar and realizes the bazaar is only there to make money, he realizes the bazaar is not some magical, exotic place. At this moment of despondency, he also seems to realize that just as he's allowed himself to be caught up in the charm of the bazaar, he's also allowed himself to be fooled into thinking that he had made a significant connection with Mangan's sister. Above all, his epiphany is that he realizes how he'd been lured by these contrived feelings.
Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger.
He is angry because he ended up feeling let down. The bazaar was just a money-making scheme and he left, feeling that his quest was not as meaningful as he'd thought it was.