Steven Fletcher has scored five of their six goals to date, with the other an own-goal courtesy of Demba Ba in the Tyne-Wear derby, and O'Neill is eager for their poor record to improve.
"I hope that over the next couple of seasons I am able to put a side out that teams actually revere," O'Neill told the club's official website.
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|7/1||Sunderland are 7/1 to beat Everton at Goodison Park with bet365|
"Defensively, it appears that we're reasonably strong. We have to create more chances and score more goals."
This Black Cats visit fourth placed Everton this weekend, a team O'Neill has the utmost respect for. The Sunderland boss heaped praise on his counterpart David Moyes, the third longest serving manager in the top flight.
"I think that you have to do pretty well in this modern game to at least hold your position but I think that sort of stability has obviously had a great effect there," O'Neill added.
"Ten years in the job is a long time and it does eventually lead to decent results. They're a very fine side, and they have been one for quite a number of seasons.
"People talk about the great start that they've had to the season but that doesn't surprise me. They’re very strong.
"We will go there to try and win the game. My own particular record at Everton is actually quite good. Anything can happen on any given day."