Gus Poyet's side beat the Premier League champions 2-1 at the Stadium of Light on Tuesday to take a lead into the return match at Old Trafford.
And while that tie is a long way from over – something O'Shea knows better than most, given his 12-year stint at United – the 32-year-old defender has asked his side to switch their attention to their league meeting at Fulham on Saturday.
Sunderland sit on the bottom of the Premier League table but could close to within a point of safety if they win and other results go their way.
"We just put this game to the side now for a few weeks because believe me, it's far from over," O'Shea told the club's official website.
"We have got a huge game against Fulham now.
"We know that if we create and play like we can do in those games we will be creating chances and we will be hurting teams. If we keep that belief, that's when we will get the wins.
"We drew 0-0 at West Ham but should have won the game; at Villa we should have won the game, so you are thinking, 'Okay, if we are keeping the clean sheets, eventually the goals will have to come for us because we are getting ourselves into such good positions'.
"It's a team game and maybe for a certain amount of time, we are thinking too individually about helping the team, in a good way as in, 'I'll be the one to help out'. But it's got to be that collective if the team is going to be successful."