Dick Advocaat insists Sunderland should feel confident they can survive after a recent positive run of form.
Advocaat believes Sunderland will build on their recent positive form and earn a win at Everton on Saturday which would put pressure on their relegation rivals.
They are suffering from a few injuries but Advocaat feels the aim remains the same and feels four more points will help his side maintain their Premier League status.
O’Shea came off during Sunderland’s win over Southampton after suffering a blow to the ribs and did not recover in time for this fixture.
The Republic of Ireland defender had played every minute of the campaign before he was forced off last weekend, and he has not managed to shake off the problem in time for the Premier League trip to Goodison Park.
Jack Rodwell is also unable to face his former club but Wes Brown will return for the Black Cats.
Advocaat said: "At training, they know what they have to do but with four games still to go, we still need four points.
"We are winning and that’s the way we go into Everton. Against good teams, they are safe, good players. It is up to us. If we can do it against Stoke City in the second half, you can also do it against Everton. It is confidence you must have now.
"As I said when we started - nine games, nine finals. We only lost unluckily against West Ham. Crystal Palace did better than we did, they were cleverer in that game, but nobody outplayed us and that is important to know.
"Against a good team like Stoke we did well. Against a good team like Southampton, a very good team, we did well. Why don’t we get confidence out of that? It’s very important."