The Black Cats ended a run of three successive league defeats when they fought back from 2-0 down to Fulham at the Stadium of Light on Saturday to claim a point.
That may have been less than O'Neill was looking for with the scrap for top-flight survival hotting up below them, and with crucial games at QPR and at home to Norwich to come before difficult fixtures against leaders Manchester United, Chelsea, Newcastle and Everton, they could certainly do with a solid points return.
However, with the benefit of experience, the Ulsterman will not set any targets.
O'Neill said: "I wouldn't want to look too far ahead. Other people will talk about this, but between now and the end of the season, we have got a pretty tough schedule.
"But starting to look into it and starting to look at points - I used to do that as a player and in the early stages as a manager.
"Sometimes it would work out and sometimes, it wouldn't, so I just prefer to concentrate on what's immediately ahead of us.
"If you look at the teams in and around us at the moment, any side in the bottom half of the table can still feel pangs of discomfort because you have still got to be looking over your shoulder.
"A couple of wins pulls you right up to mid-table; a couple of losses, as we have experienced, and you're having to look over your shoulder."
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