Jap is a pejorative term like nigger, kike, spic, wetback, towel-head, etc. Let's say Bill said, "No disrepect to the Jews, but we ran some kike plays today". Same thing would happen.
What constitutes a slur is really a separate discussion, and the only argument on behalf of Parcells that could be made - that "jap" is not a slur. Most Japanese would disagree.
What makes a slur a slur is not some P.C. mythos, but the simple fact that people use it as such--to degrade or knock down others. You don't call some latino stranger a spic to his face upon first meeting him do you? Why not? You don't call some black guy nigger (well, maybe if you're black you do but that's another discussion for another time).
Oh well, big messy subject, people's feelings, dignity, sense of self and racial/social place, etc. are involved.