Tulane is in the AAC (just won the AAC championship yesterday actually) but you're right that loss did hurt as did their loss to Texas (a team both TCU and Alabama beat). Still, the fact that they even got near the conversation of the CFP is a pretty incredible accomplishment for Klieman, his staff, and his team.
I think I saw it on Twitter yesterday that this is K-State's first 10 win team not coached by Bill Snyder since 1910.