In the immediate aftermath of the War of 1812, Native peoples in the Upper Midwest (what was then called the Northwest) and in the Southeast (then the Southwest) suffered almost immediate consequences. The war all but destroyed the power of many of the Native people in the Midwest, as most had fought alongside the British. This paved the way for American expansion into the territories that became Indiana and Illinois, and later Wisconsin and Michigan. Something similar happened in the old Southwest, where the War of 1812 encompassed a civil war among the powerful Creek people. Their power was broken by this conflict, and they, and other native peoples in the region, including the Cherokee, Choctaw, Chickasaw, and Seminoles, were driven from their lands over the two decades that followed. The states of Alabama, Mississippi, and Louisiana were established on lands taken by force and by treaty from these Native peoples. So the War of 1812 opened the way for US expansion, which by the outbreak of the Civil War, resulted in the removal of almost every large group of Native Americans east of the Mississippi. So in a very real sense, US expansion pushed Native Americans off their lands.
The expansion of the U.S. after 1812 was a major tragedy to the Indians living west of the Appalachian Mountains. The treaty that ended the War of 1812 meant that the British left the Great Lakes region; the Indians in that area lost a key ally. Tecumseh's movement to unite the tribes in order to resist white encroachment died away soon after the Battle of Tippecanoe, and the movement ended for good when Tecumseh was killed at the Battle of the Thames. Native tribes signed harsh treaties with encroaching whites giving the United States free title to the Northwest Territory. The United States also expanded further south in search of farmland—within a generation after the War of 1812 the Five Civilized Tribes would be pushed across the Mississippi River into present-day Oklahoma in what would become known as the Trail of Tears.
The expansion of the US population in the years after 1812 was to have a huge impact on Native American populations. In general, it pushed them out of their own lands and then out of the lands that had been given to them when they were removed from their original homes. It ended up causing them to be isolated on relatively small reservations that were often in very inhospitable areas.
After 1812, America acquired areas like California and Oregon. The overland trails (and eventually railroads) to these new acquisitions helped also to bring more Americans into the area acquired in the Louisiana Purchase in 1803. As more and more Americans moved into these areas, Native Americans were displaced. For some, this meant being displaced from areas where they had been sent during the Indian Removal of the 1830s.
Eventually, this expansion led to a situation in which Native Americans were largely confined to reservations in out of the way areas that were least useful to white people.