The Black Cats came from two goals down to claim a point, with Stephane Sessegnon firing home the leveller with 20 minutes left.
"It was certainly an incident packed game," admitted O'Neill.
"We have conceded a penalty and then the second goal was, from our own viewpoint, very poor - but we fought back and we could and should have won the game.
"I cannot be disappointed in the effort, we had to go for everything and there was always that chance we might concede as we were going for the win, but we had enough pressure and enough balls going in the box to get something else."
Fulham's two goals came in the opening 35 minutes and were from counter-attacks, the second direct from a Sunderland corner.
"It was very poor and poor organisation by us and that is down to me and I was disappointed, the last thing you should be doing when the ball is dead and going into their box is picking the ball out of your net a few seconds later," he said.
Whilst both teams were given penalties, O'Neill bemoaned the fact that they were not given further spot-kicks as both Philippe Senderos and Emmanuel Frimpong both looked to have handed the ball late on.
"These things are important, I don't want it to be a moan or a rant, but last week we had two penalties and then again today," he said.
"In general there are a lot of soft penalties being given, 20 years ago maybe the game would not have had a penalty today but this is not 20 years ago this is now and these are the directives we have been given, and from the referees."
O'Neill was full of praise for Stephane Sessegnon, who turned in a Man of the Match display.
"We said a few weeks ago if he could add some goals to his game he would be priceless and he is doing that," he continued.
"He has been terrific and is full of confidence at the moment and has been big player for us recently."
He was also pleased with goalkeeper Simon Mignolet, who produced a crucial save at 2-1 from Dimitar Berbatov, which they then broke from and equalised.
"It is an important save, Fulham were maybe going 3-1 in front and it would have been a long way back and then within 20 seconds we have scored and made it 2-2, he has come up with some big moments this season and that was terrific, a big moment in the match," he said.
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