I don’t see his use of the concept of regret as a moral statement as much as it is a cognitive one. As he says, to regret something is to wish that the past and present are different than they are. You could dispense with the any whiff of moral content and substitute the simple thought that something could have been different. The assumption of determinism does commit one to the idea that things could not have been different. That we can think that it could be, and even more could wish that it could be different, is an inherent disproof of determinism for the human mind and soul.