....and it certainly includes all these elements which have been mentioned in this thread, but I do think that his mortification ALSO arises, in part, from his realizing that he has publicly dissed the girl he finds so attractive, and who is yet so far beneath him socially, and that combination, in and of itself, can generate lots of mixed feelings and mortification!

At this point in the novel, we have no reason to believe that he is a social ignoramus, a man who does not know what a gentleman should and should not do. So it is fair to presume that he knows the rules, he knows a gentleman would, soberly reflecting the following morning on what he said the night before, intending Lizzy to hear it, find some appropriate way to apologize for what he said.

But I assert that Darcy's self-talk, reported by the narrator, does not cover the full range of thoughts he might be having and/or repressing. He could reasonably be mortified at the prospect that if he does apologize, maybe she'll tease him (and perhaps he even overheard her making light of his putdown later that evening)? Or he could be worried that maybe his apology will be misinterpreted as a veiled come-on, either by Lizzy herself or by someone who hears about it from Lizzy (in that regard, he does not know if Lizzy is discreet or not, perhaps Lizzy would tell Jane---and I believe she would---and perhaps he's worried that Jane would tell Bingley, and that would be embarrassing to Darcy)? Or maybe he does not trust himself not to betray his attraction at that moment? Or maybe he can't figure out a socially proper way to relay an apology to Lizzy, since young men are not supposed to send letters to young single women, right?

In short, Darcy's mortification could be very complicated.