I was unaware that anyone seriously doubted that the UK was the victor of this war... I know every now and then you get the nutjobs saying "America has never lost a war, ever, and Vietnam was a Police Action and the UN lost in Korea not the US, so, we're perfect, yah", but I thought that it was pretty common knowledge to most of the normal populace of the States that they lost this one. It's certainly common knowledge in the UK and Canada.
Now, I'm not claiming that the war was a stunning victory or shattering defeat for either side. It was, as most history books say, a fairly unimportant war in general -- it did nothing to prevent either the States from starting their Manifest Destiny policy a few years later, nor the expansion of the British Empire to dominance in the world and the defeat of Napoleonic France. I'm simply setting the record straight for history. I do also believe that it's important to note the details of history, as well as the grandiose themes, as the smaller actions in history are what comprise the major ones.
On to how the British claim victory. In regards to territories claimed by the British empire -- significant swafts of land in present-day Minnesota, Michigan and Wisconsin were under a treaty that provided for the housing of Canadian/British troops, and several forts (the only one of which I can name by heart is Fort Mackinac), as well as the permanent disbandment of Fort Dearborn -- which was retrospectively actually beneficial to the Americans, as the location would later become Chicago. However, the most important reason the war must constitute a British victory is that the war was an offensive action by the Americans, who tried to seize all or part of Canada -- resulting in repeated repulsions, and territorial losses by the Americans by the end of the war. It's a fallacy of wars like this one to believe that returning to (nearly) status-quo ante-bellum concludes a tie -- because one side is always the aggressor, and the other, the defender. When an aggressor attempts to seize a castle, say, and the defenders successfully repel the attack, what is the outcome of the battle? It is not a draw, but rather a victory for the defense. To add the icing to the American-defeat-cake, so to speak, the US suffered several incursions into the pre-war territory constituting the US, and, as everyone knows, got their capital pillaged and the White House burned to the ground.
American goals at the beginning of the war were to seize what they could of Canada (American expansionism), and end the impressment of American sailors by the Royal Navy. While impressment largely became a moot subject by the end of the war, as the Brits had defeated Napoleon and needed no more sailors, the United States absolutely failed in its main pre-war goal of annexing Canada. Thus, Canadian victory was absolute, even though territorial gains were largely negligible.
In sum, the US absolutely lost the War of 1812, because it, A. Failed to invade and conquer Canada, B. Failed to repel the British troops in America, C. Gave up several forts to the British in the Great Lakes region, D. Lost their capital, and F. failed to stop impressment by the British Navy.
American loss.