Sunderland crashed out of the FA Cup in the fifth round over the weekend, eliminated by League One outfit Bradford following O'Shea's third-minute own goal and Jon Stead's second-half strike.
With pressure mounting on manager Gus Poyet and Sunderland securing just one win from their past eight Premier League fixtures, the Wearside team face fellow strugglers West Brom in what is shaping as a crucial match for both teams.
Sunderland, who hover just two points above the relegation zone, are two points adrift of West Brom.
And O'Shea has called on his team-mates to put Sunday's result behind them as they bid to preserve their Premier League status.
"We have to forget Bradford very quickly and focus in on the job in hand. We need to stick together and move on," said O'Shea.
"We're already looking ahead to Saturday, and because of what's just happened, whoever we were playing next was always going to be a big game. There needs to be a reaction.
"The fans will want to see that but, as players, we're all aware of the need to react positively too. There's no panic here or anything like that – we're all on the same page, sticking together and hopefully getting three points.
"Last season had lots of ups and downs, so in a way we're used to dealing with that. It's about staying calm and sticking to what we do – the more continuity we have, the better we'll play.
"We have to make sure we dust ourselves down, see what kind of squad we have for the weekend, and then make sure everyone is fighting together for the same goal.
"There's a real determination that none of this will get in the way of what we have to do. Last season, people were saying that the cup run would be a distraction from the league. Now, there's no cup any more so we'll be fully concentrated on the league."
