The Black Cats improved dramatically when O'Neill took over from Steve Bruce last season but find themselves sitting 16th on the table, just four points above the bottom three.
With that in mind, and the fact Sunderland have netted six goals in nine outings, O'Neill fears that this could be a season where the Wearside club may have to stave off a potential drop but he is hoping to turn things around following his positive beginning.
"We have our own statistician in here and he tells me it depends who you look at," he said ahead of tomorrow's trip to fourth-placed Everton.
"But what doesn't lie is the number of goals that we have scored.
"What we have to do is have more shots at goal regardless of whether I believe or don't believe the stats, and I don't need anyone to tell me that.
"We are playing reasonably okay but we need to be more incisive.
"I don't believe we have ever been prolific in that area but we do need to create more.
"I have not completed a full season here yet. It just takes a bit of time, and by hook or by crook I intend to make this a team that the supporters are genuinely proud of."