Disgusted (adj) means ‘feeling or showing disgust; disturbed physically or mentally by something distasteful; cause (someone) to feel revulsion or strong disapproval; severely disappointed at someone or something:
We were disgusted at her incessant lying and cheating on her husband.
I am totally disgusted at you for not feeding our dog as punishment.
She is totally disgusted by what has happened.
There is a whole world of sycophantic and biased television that I am disgusted by.
We were absolutely disgusted with the way both teams behaved just after the match ended.
The Vice-Chancellor was disgusted at/with the way the police treated the students.
Mr and Mrs Franklin said they were disgusted at the situation which had left them speechless.
I was disgusted at the way the man seemed to be more concerned about his car than the victim of the crash.
They were disgusted by the violence in the campus.
Mother was disgusted by Joe’s failure.
Parents were disgusted by the glorification of violence in the movie.
He was so shabbily dressed at the party. I tried hard not to be disgusted by his appearance.
He’s disgusted by all the promises political leaders made at the time of elections.
Most locals were disgusted by the way the protestors had blocked the roads.
I am disgusted with you.
She’s totally disgusted with Bob’s behaviour.
He was disgusted with the Jury’s decision.
Jane was disgusted with the Idea of travelling by car instead of train.
My wife was really disgusted with this idiot native who had just spat on our car.
The minister was disgusted with the way anti-CAA protesters had been behaving.
Father didn’t say one word to Paul after he got bad grades in school because he was absolutely disgusted with him.
I’m absolutely disgusted that anyone should be attacked in this manner.
Wilsons were so disgusted that whatever faint chance of their granddaughter’s return is left would disappear forever.
Given all above examples, both prepositions ‘by’ and ‘with’ can fill the blank in the opening sentence while ‘at’ is less likely to work.