He feels however he feels, but I still think he should apologize. There is no point to keeping a part of the fanbase where you went to school upset at you. Just say something to the effect of "I loved my time at NT, and that will always be my school", and then be more careful about his tweets in the future. He doesn't have to specifically say he was rooting for NT over LSU, or anything like that, particularly because that would be a lie.
Nothing we say on a message board is going to change his mind, but he certainly has an opportunity to please all parties involved....especially considering the LSU fanbase probably doesn't know, or care this is even happening, and he may or may not care what they think anyway.