The Gunners dominated possession, particularly in the second half, but the visitors held firm and were able to start the season with a hard-fought point and a clean sheet
The Black Cats defended stoically for 90 minutes as the hosts dominated possession but failed to find a way through.
Sunderland had a few chances of their own to win the game as neither side was able to grab the winner, but O’Neill was delighted to start the season with a point away from home.
"It was a great point for us and I’m obviously delighted with it," he told Sky Sports News. "I would have taken it before the game, especially considering our circumstances with the players we had today not all being fit.
"So overall it was a fantastic effort. Of course we’d like to rectify situations by getting some goals. Playing Arsenal any time is pretty difficult but today was a magnificent effort."
The Black Cats have not won at Arsenal since 1985, and several players had chances to give Sunderland the points, particularly in the first half as the hosts cut frustrated figures.
"I thought we had some good chances in the first-half ourselves," O’Neill added. "As we got tired in the second half obviously we had to defend closer to our own penalty area and that became more difficult.
"We stuck to the task and we did brilliantly. It’s a point on the board away from home and it gives us something to go forward."