There is a quality assurance approach or theory from W Edwards Deming that needs to be absorbed by institutions, and it’s that everyone is trying to do their best job and it's the machinery that is getting in the way or creating barriers. Most errors arise from processes but anything in an organization could potentially get in the way. One role of a manager is to work to remove these barriers.
You should demand any negative feedback provided is specific and try and see it as someone taking the time to try and help. Given that someone is trying to help, ask questions you can use to improve things and see the feedback giver as a person who has knowledge you lack and can gain.
You also have to be prepared that you will get unskilled feedback and that is a different opportunity for you to stretch leadership muscles.