I think many times there is difference between what a person says and what they actually feels. He does not regret that he killed Sadeas, he says that explicitly but he also thinks, as I remember, that he failed his father. He also wishes that he could have killed him in a proper duel honourably instead of a dark alley.
But what I wanted to say more was that killing someone, in many magic systems, is considered an act that opens your soul up a little. He also begins to think that he is not the son his father deserves.
anyways, his self doubt, he says his killing of Sadeas proves that he is not worthy of being a king, along with the subsequent reveals about Rathalas and his mother, have the potential to really break him. He, and Renarin were very close to her. Plus he might now feel that his killing Sadeas proves that he is exactly the son his father deserved.