Gus Poyet's side have two games left to play this season and, regardless of their results, they will be safe if Norwich City fail to beat Arsenal on Sunday.
However, Sunderland have been in such excellent form in recent weeks that O'Shea does not want to have to rely on others at this stage.
The Black Cats face West Bromwich Albion on Wednesday and Swansea City on the final day, and O'Shea is confident of following up Saturday's 1-0 win at Manchester United with another couple of good performances.
"We're not completely safe but we've got two home games now," said the defender.
"We want to make sure we get the results which mean we've earned the right to stay up, rather than worrying about results elsewhere.
"The confidence and attitude in the camp is fantastic and if we play anywhere near the standard we played against United, we won't go far wrong."
Sunderland's victory over United was their first at Old Trafford since 1968, and O'Shea was thrilled with their performance against his former club.
He said: "I couldn't have been prouder of the lads for the way they performed all over the pitch.
"We showed what we are capable of, battling all the way to the end to ensure we got those three points.
"I was a United player for a lot of years and it feels good to go back and do as well as we did."