Remember the look on his face when he won? He was horrified! Same when he first met with Obama and they had a joint press conference. His body language was like, "oh fuck, what am I even doing here."
I think regret is hard for him though, because to regret something means you have to feel, in some way, you could have done something better or differently. You have to take ownership of bad feelings and in your part of bad outcomes. I just don't think his brain will let that happen. Everything bad is always someone else's fault.
But yeah...maybe in some dark, cobweb encrusted corner of his mind, he wishes he was just a NY scam artist and fake "tycoon." It served him well enough, as you noted.