What is the professional way to respond to criticism from your supervisor?
The best way to respond professionally to criticism is to see it as an opportunity to improve, not as an attack upon you or your abilities. When a supervisor criticizes you, you should listen carefully to the criticism. You should pay close attention so that you understand what suggestions are being made. If you do not understand something, you should ask questions. As you ask, you must be sure that you are asking in a way that makes clear that you are seeking guidance rather than trying to defend your actions and attack the supervisor's criticism.
If you feel the criticism is unwarranted, you should come back to the boss later, in private, to discuss the matter. You should say that you do not understand the criticism well enough. You should say why you did what you did and ask for clarification as to why it was wrong.
In all cases, it is important to act as if you are trying to improve, not as if you are angry about being corrected.