Disgusted here is how you feel when something is so wrong, so unfair, or so not-OK that you are very angry and upset. A lie, someone being cruel, a filthy kitchen left for others to clean, a government that breaks a promise — people say they are disgusted. The feeling sits in you. British speakers especially use it for hot disappointment and anger (“I’m disgusted with the government”), a stretch from “this makes me sick” toward “I am fed up and this is not acceptable.” American speakers do this too. Though actually, the same word also covers the body feeling: a smell or rotting food that makes you want to turn away. That is the older picture, and it is still alive. In both uses, disgusted by often points at the thing that caused the feeling; disgusted with often points at a person, including yourself.