O'Neill was given his marching orders after striding on to the pitch at half-time to remonstrate with ref Steve Bennett.
Fulham led at the interval through a Clint Dempsey goal but an inspired second-half performance was capped by Shaun Maloney's winner in the first minute of injury time to give Villa their first victory of the campaign.
"I should have waited until we got to the privacy of the dressing room. I thought - probably wrongly now - that a Fulham player was down injured for the two minutes' extra added on at the end of the first half.
"The referee told me at half-time that he had played two and a half minutes. I apologise to him. I should not have remonstrated like I did.
"It was different watching the game from up above - but it would have been an injustice if we had not have won.
"We were exhilarating going forward and the crowd stayed with us to the very end."
O'Neill admitted he had required a club steward to relay the message to the dug-out to bring on Maloney for the final seven minutes.
O'Neill said: "There are these new sort of phones I am incapable of using so I got the steward sat next to me to send down the message to put Maloney on.
"I thought the game had gone on too late for us to score but it was a great ball from Ashley and, knowing Shaun from his Celtic days, I was confident he would finish.
"I thought Ashley was sensational. When he is in that type of form we always look capable of scoring."