The Black Cats were thoroughly outplayed for long periods of the match, but managed to hold on for a potentially-valuable point.
"It was a tough fixture for us," O'Neill told BBC Sport. "We haven't got all our players in place, and we are hoping to add players shortly.
"In the sunshine we got very tired and with Arsenal forcing the issue, we are happy to get a point."
Sunderland's next match is against Reading at the Stadium of Light on Saturday, August 25.