Clay was in favor of Texas annexation, which gained him votes in Tennessee and North Carolina, but also cost him votes in New York, which ultimately cost him the election.
Yeah, but Polk was also in favor of TX annexation, and more strongly than Clay. Since this was a popular position in TN, by logic Polk should have won the state.
They both supported it and hence both got and lost support because of it. Just because Polk personally felt stronger about it doesn't gain him any more votes than it would Clay. I don't see how that is "logic" at all.