Two goals from Fernando Torres and one from Juan Mata put the Blues three ahead by the 49th minute before Adam Johnson grabbed a 66th-minute consolation for the Black Cats.
Tuesday night's re-arranged home clash with Reading now assumes even greater importance for O'Neill as he attempts to turn around a run of just two league wins in 23 games.
He said: "We have dropped into the bottom three and the game that both Reading and ourselves have in hand, on Tuesday night that's over, so from that viewpoint the league will be level.
"It's a tough fight, though, it's a really tough fight.
"We got some fantastic results last season and it seemed by mid-February we had calmly taken ourselves out of the relegation problems. I never saw it like that. I thought every game was a fight and it is exactly that now.
"Every game is a fight for us and we need to, when we have a foothold in games, try to make it count.
"That's the major point."