The Northern Irishman, who took over at the Stadium Of Light last December, led the club out of the bottom three to safety and feels that there is a lot more that he can achieve with the current squad of players.
"I want to do really well here at the football club," the former Celtic boss told Sky Sports. "There is a timescale because I have a contract and, if I have not lifted the side into a proper position, I will move over and give it to someone else who would be better equipped. But that hasn't happened yet.
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The Black Cats, whom O'Neill guided to a 13th-place finish last season, go into Sunday's game against Fulham clear of the bottom three only through goal difference. But the manager is taking inspiration from his own former boss, Brian Clough, at Nottingham Forest.
"It sounds crazy but, before Peter Taylor joined him, he had a year-and-a-half at Forest where he did not improve the team one jot. We may even have gone backwards," explained the former midfielder, who made 285 appearances for the club under Clough.
"We were struggling as a mid-table Second Division side until Peter joined up with him and he got renewed vigour.
"We had plenty of bad times and he just told us to stick in together. Lesser managers probably said the same thing but, when he said it, you felt there was something behind it. And that is what we must do and we'll come through it."