I had a horrible extraction last week with a v compilicated root that menat that the dentist had to get it out in several pieces, but the dentist had put big injections in on the outside and inside gum, and I couldn't feel anything, bbut the noise and general grappling were still horrible...many sympathies for your son.
Was the dentist aware that it had not been fully anaesthetised? It may be worth reminding him and asking if there is anything he can do to improve the level of anaesthetic effect.
Also, I wonder if you can give him a good dose of paracetamol and nurofen before he arrives at the dentist so he is 'painkillered up' for when the anaesthetic wears off.
If it was really bad for him, I would consider asking about a GA.
I usually say to DS about any procedure 'the Dr / dentist / physio / nurse will do all they can to make it more comfortable, I don't know what it will feel like, but if it does hurt, it will be over very quickly'. Also get your DS on board that he wants it done for the long-term benefits, and fully understands what those are - IME children who feel less 'victiised' feel less vulnerable, less afraid and therefore less panicked by pain.
(this is based on DS having had much bone surgery AND a blimmin dental surgery!!)
Good luck - this sort of thing is agonising for parents, but the calmer you can force yourself to be, the better.