Why would Kirito care about killing some douche that just murdered someone in front of him and then tried to take his life? Not everyone has some traumatic breakdown after defending themselves so that criticism is a bit of a reach. I haven't read the light novels but maybe they touch on it there, why waste time and budget listening to the two main characters talk about how they "feel" after doing what needed to be done to a villain?
Also, the show uses a lot of timeskips. I'm not exactly sure how much time passed in-between the duel and sex scene. Maybe someone else could elaborate.
If you think of yourself the way kirito clearly thinks of himself, a lack of reflection on the fact that you killed a guy is pretty jarring.