Saturday's 3-1 defeat at QPR brought the bottom side to within seven points of Sunderland, whose cushion on third-bottom Wigan is just six points.
Next week's home game against Norwich - three points better off on 33 - is now taking shape as a huge fixture ahead of successive games against Manchester United, Chelsea, Newcastle and Everton.
And O'Shea said: "We have to pick ourselves up very quickly.
"We had a great start to the game and led 1-0 but they got a bit of luck for the equaliser - the ball hit the inside of my foot after Andros Townsend had mishit his shot and fell right to Loic Remy, who tucked it away.
"Townsend scored a pretty good goal to put them 2-1 up but we definitely should have done better with the last goal. Even with the second goal, we could maybe have stopped it beforehand.
"If we'd done that we would have caused QPR a few more problems because the home crowd were getting tense. We needed to be cleverer with the ball.
"We have to front up now. We have a big week and the Norwich game is building up to be massive."