The Ulsterman saw his side win for just the second time in 19 attempts as they saw off 10-man Fulham 3-1 at Craven Cottage on Sunday to ease their fears of being dragged into the relegation zone.
They entertain high-flying West Brom on Saturday hoping they have emerged from their early-season lethargy and can now start pushing their way up the table.
However, O'Neill knows they, like so many of their close rivals, cannot relax for a moment.
He said: "There are a number of teams who start the season and never contemplate anything else other than being in the big league, your Manchester Uniteds, your Chelseas, Manchester City and a few sides like that.
"There's a group of us and it's a fight, and it's a fight every single week until you have got the requisite number points on the board.
"Only then can you start looking up the table. But I think teams will always be looking over their shoulder until they get the points on the board and start winning some football matches."
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