Yohan Cabaye had given the visitors a third-minute lead, but they had to play with 10 men after 65 minutes when Cheick Tiote was sent off for a foul on Scotland striker Steven Fletcher.
Then, to the relief of the Sunderland fans, Demba Ba netted an own goal with just a few minutes remaining.
O'Neill said: "When we equalised, it was one of the best moments, it really was, and to be accompanied by that noise was wonderful.
"There's an element of relief, but every derby game I have been involved in either here or in Scotland [with Celtic], there has always been an element of relief.
"In the second half, sheer pressure alone probably yielded us the goal rather than anything flamboyantly brilliant.
"We got the goal and maybe had enough time then to go on and win it.
"But in the circumstances with Newcastle being down to 10 men and having defended so strongly, that would have been harsh."
Newcastle boss Alan Pardew likened Fabricio Coloccini to England's 1966 World Cup-winning skipper Bobby Moore after seeing his captain turn in a superb display before going off injured. Pardew said: "Maybe if Coloccini had stayed on, he would have seen it out. He was phenomenal.
"If you want an example of a centre-half playing where you have got to head it, kick it, cover people, get in the right position and then have the calmness to play, that was your example. He was like Bobby Moore at his best."