Notre Dame's superiority complex and financial greed kept them out of the playoffs today. Nothing else.
They could have chosen to join a conference but feel they don't need to. Had they joined the ACC instead of just playing an abbreviated ACC schedule, they would have been in the ACC championship game and would have been one of the 5 highest ranked conference champion (potentially). They want to be treated differently than all other major programs and that "special treatment" kept them from competing for the title this year.
Personally, I love it, for 2 reasons. Force them to join a conference. They are NOT above every other football program AND I think they could have been a major problem in this post season.