In absolute numbers, you are correct when you say the US lost more. But the Indians lost a far greater percentage of their already tiny population. They could not afford this, and were the only party to lose land as a result of the war. The notion of a British invasion is silly. The British were fighting an unstoppable army in Europe and cared almost nothing for this war. It was the Americans who started the war when they invaded British Canada thrice.
The war of 1814 represented another loss of land control and sovereignty of the American Indians living in North America. Each time a battle was lost and new political boundaries were drawn, the American Indian lost. The war of 1814 is no different than any of the early American Territorial wars on this continent.
Yes, I do think that they were the ones who lost the most during the War of 1812. They lost a huge number of warriors, and after this war everyone turned on them and took away all of their lands, and ended up not appreciating their help in any way.
During the war of 1812 the American Indians suffered such a loss of people and land, they have not been able to recover from it. Ever. It still plagues them to this day. After studying world history, there is on one group of people who suffered more than North American Indians.
Some historical analysts would suggest that the American Indians lost the most due to the outcome of the war of 1812. Had the Americans lost, they would not have taken control of the northern continent, and thus the American Indians would not have been treated in the manner that would come later. What is typically not considered is the Spanish may have been just as cruel if not worse than the Americans. They certainly had a history of native brutality in the southern continent.
No, the American Indians were not the biggest losers in the War of 1812, because Britain suffered the biggest loses. Britain wanted to have a do-over of the revolutionary war. They came back to try again, and again they were not successful. The American Indians sustained losses, but no more than the United States did in the conflict.