The Black Cats appeared to be heading for a defeat against the Potters on Monday evening when they were down to 10 men after Craig Gardner's red card, and trailing 1-0.
However, they produced a much-improved second-half display and earned a vital point in their relegation battle thanks to O'Shea's 63rd-minute equaliser.
O'Shea said: "It shows the players really want to stay in this league. They want the fans to get behind us, we want Sunderland in the Premier League next season.
"The effort we showed in the second half and the passion and the commitment, all the cliches in the book, we need them all again on Sunday.
"We know we still have it in our hands and there are lots of other teams as well, not just ourselves, Norwich, Southampton, Newcastle, Fulham - there's still a lot to play for."