|The irony is that your manager is the one who needs negative feedback. Public reprimands are totally unacceptable, and inaccurate public reprimands are nothing short of heinous.|
However, it is important for you to take an honest look at your performance. Although airing dissatisfaction in public is patently wrong, are you absolutely certain that your job performance is strong?
Assuming that your work is up to par, you need to revisit the strategy you are using to combat this bully. You should defend yourself and your work, but if you are jumping back at your manager, you are playing into his hand. You are probably emotional in these rebuttals, and he can use that to his advantage.
While you need to let him know that his comments are inaccurate and inappropriate, you should pick a better time. You can have more of an impact by meeting with him in private as soon as possible after his attack.
This will allow you to gather yourself and your facts, and then give him the truth about the work he criticized, plus the truth about the impact of his public reprimands. Make sure he understands that you want this treatment to stop immediately. Your next step will be determined by his next step.