We started a war and got our capital sacked. I know that not much changed from the status quo, but it's hard for me to call that anything other than a loss.
So? Unlike most European wars where the capture of a capital was usually the last ditch battle of the losing army, the capture of Washington was merely a raid where the British relinquished control of the city within 24 hours. Sure it was a humiliating defeat of a single battle (or rather the Battle of Bladensburg), but it meant little strategically for the overall war or the ultimate Treaty of Ghent.
Besides, does that mean America similarly raiding and burning Canada's capital (York, nka Toronto) mean Canada lost the war?
We started a war and failed in our operational objectives, both official and unofficial. The fact that we lost the capital only serves as a reminder of how badly we did at what we had set out to do.
It is important to note though that there are differing standards for differing times. The fact that no territory was exchanged might mean it could be considered a draw by the standards of the time, but as someone speaking from a modern perspective I would tend to qualify it as a loss. I don't usually judge older times from a modern perspective, but considering how cavalier people then and now can be about war and warfare, I tend to make a certain exception for this in terms of being critical towards the old standards of warfare.