They say home is where the heart is, and for Vahan, that's with his family—so though he thinks that once he gets to Constantinople everything will be all right, it's simply not the case. The horrors that he's seen and the deaths he's experienced are all still with him, so while Vahan is in a different place, he's still in the same state of mind. In the end, he finds peace by visiting a graveyard where he imagines his family's souls are. Tragic much? We can't help but feel sorry for Vahan throughout the whole book, so it makes sense that the ending follows suit.
He suffers a whole lot, and a feeling of emptiness follows him wherever he goes. Even though it's heartbreaking, it's important for us to feel this with Vahan, because every home he's ever known has been taken by the war. Vahan's only home now is in his mind, where he connects with his family through memory.