However, although the Black Cats are not mathematically safe just yet, O'Shea has revealed that the team will travel down to fellow strugglers Aston Villa next Monday believing that they can collect a positive result.
"The next four games, the performances that we have shown, we are confident going into these matches," said the Republic of Ireland international.
"If we can get something down there, hopefully that should see us across the line. We have got two home games then against Stoke and Southampton and a tough away game, so the sooner the better, as they say."
Sunderland have failed to win any of their last three matches against Villa.