The win was only Sunderland's second of the season, but O'Neill believes that they nearly cost themselves the match with a few mistakes.
"The sending-off had an effect on the game," said O'Neill. "It gives us that advantage. Whether we're able to take care of that advantage is another thing but I thought in the second half we were able to do that. We made some really elementary mistakes at different stages in the game. [We were] unable to really kill it, always having Fulham in the game.
"We mentioned at half time the importance of keeping calm, keeping possession and trying to stretch Fulham if we can possibly do that. From the viewpoint of getting a few goals it has worked out well. I suppose it led for great excitement but, in fact, it'll do your brain in but I'm just delighted to have won and delighted to have scored a couple of goals.
"You must win as often as you can in this league because there is nothing like it. No other feeling can beat it and the players are delighted."
Sunderland host West Bromwich Albion in their next match on Saturday.