The Hammers controlled much of the match and recorded 20 shots on goal to the Black Cats’ four, but O’Neill’s side were heading for the win before Kevin Nolan denied the away side in stoppage time.
Following the dramatic finish at Upton Park, O'Neill told reporters: "The manner in which the goal was scored, and obviously the timing, were obviously disappointing. Just when I thought we’d seen it through...
"We looked as if we dealt with just about everything they had thrown at us, and we were never able to kill the game off.
"We still had those great opportunities to score, particularly in the second half, and as West Ham were pressing forward, leaving the door open, with a bit more care we should have taken advantage of that.
"I know they were on the break, but [we were] two versus two on a couple of occasions, and there was a great ball by [James] McClean when I thought that David Vaughan might have scored."
Steven Fletcher had given Sunderland the lead inside 10 minutes after controlling Sebastian Larsson’s long ball before finishing with a firm left-footed strike past Jussi Jaaskelainen from an angle and O'Neill is dleighted with the impact made by the former Wolves man.
|BLACK CATS OUT OF LUCK|
|20/1||Sunderland are 20/1 with PaddyPower to be relegated from the Premier League this season|
The Ulsterman added: "He’s playing brilliantly for us, not just the goals. He’s scored all of our goals obviously so far, but it’s also the rest of his game. He’s bringing players into play, giving us a little bit of respite and proving himself an all-round centre-forward."
The Black Cats have now drawn all four of their opening league matches, and O’Neill lamented his side’s failure to stay tight at the back despite previous defensive displays.
He concluded: "I thought we should have won the game.
"Today if we’d won, with three games away from home, it would have been a really good start to the season for us. But we just have to try and win a game. Obviously I think this side is capable of doing so.
"Of the other three games we’ve played, in the first game of the season against Arsenal we were under pressure possibly of a different kind and we saw it through, and against Swansea when they were flying high at the time, and Liverpool who definitely had the better of the second half."