The Black Cats remain six points clear of the Barclays Premier League basement battle despite having taken a paltry two points from their last six games.
Asked if today's clash with Norwich City has added pressure, O'Shea said: "As professionals, it shouldn't do. Why should it?
"There are 90 minutes in a game of football - if it's 0-0 in the 75th minute, there's no problem.
"We are more than capable of scoring goals in the last 10 minutes as well as the first 10 minutes.
"It's going to be important on Sunday that the players stand up with bravery and composure and the attitude to come and take the ball, come and want to play, want to play football and not hide and shy away from the challenges that we face."