[Ibrîniðilpathânezel]

I think that if Sauron suffered because of the loss of the Ring, it was not the same kind of torment that lesser bearers of it would have felt. Sitting there for three thousand years without it, his "torment" would have been, I think, bitterness and anger, mostly directed toward the Men and Elves who deprived him of his Ring and its power. I rather doubt he would have consciously blamed himself for not considering the possibility of its loss, but like most profoundly bitter and angry persons who are in denial of their own part in their current circumstances, it would have gnawed at him, even unacknowledged. And yet, that bitterness and anger often comes to dominate the lives of those who will not let go of it.

So did he feel some kind of torment over the loss of the Ring? Psychologically, yes, I imagine he did. Was it the kind of suffering for which I could pity him? Not really, no more than I could feel sympathy for an abuser who is upset because his victim finds a way to stop the abuse. Of course, there's a huge amount of personal experience behind this train of thought, so take it as you will.