The 45-year-old Italian, already fuming at a disallowed Jozy Altidore goal which would have levelled the scores at 2-2 with 20 minutes remaining, was incensed at the length of time it took Olivier Giroud to leave the pitch as he was replaced by Chuba Akpom.
However, his efforts to persuade referee Martin Atkinson to hurry things up simply landed him in hot water.
Di Canio said: "I never was calmer than today [Saturday], even with this wrong decision. I said only that the opponents' player took two minutes to walk from the middle of the field, 40 yards.
"We lost time and I invited the referee, I tried to persuade him to push him quicker out because there was four minutes of added time and we had a free-kick at the edge of the box. You never know what is going to happen.
"That was my protest. I said, 'You have to tell them to go out quicker'. The problem was that he told me, 'If you keep going with your mouth, I will send you off, I will send you up to the stand'.
"My mistake was that I invited him. I said, 'If you want to complete a perfect job today [Saturday], you have to only send me off'. He said, 'Go off'. They were the words.
"I am sure that he is a good, a good professional. I can recognise that he made two mistakes: the first one at this crucial moment, the second one, I don't know if it was a mistake from his point of view because he would probably say, 'You invited me to send you off, I sent you off'.
"We can smile now, but that was our conversation - 'If you want to complete a perfect job, you have to only send me off'. 'Now you go up to the stand'."