The Black Cats' skipper led his troops to a famous 2-1 semi-final, first leg victory over former club Manchester United on Tuesday night which gives them a fighting chance of reaching their first major final since 1992 when they head for Old Trafford on January 22.
However, O'Shea and his team-mates face crucial league clashes with Fulham on Saturday and Southampton before then, and dragging themselves from the foot of the table and out of the relegation zone will be the only focus for most of the next fortnight.
O'Shea said: "Look, we have got to know now that the games that we have, if we do create and play like we can do, not that we will be okay, but 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 went away to West Ham, we drew 0-0, but we should have won the game; we went away to Villa and 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 about making that right decision of whether to shoot first time, pass to a team-mate and making sure. When a team goes 1-0 up, it's everyone.
"It's a team game and maybe for a certain amount of time, we are maybe 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.
"We just put this game to the side now for a few weeks because believe me, it's far from over. We have got a huge game against Fulham now."
Despite their lowly league position, confidence coursed through Sunderland veins as they took the game to United and ultimately added their scalp to those of Newcastle, Manchester City, Chelsea and Everton, an illustration of the inconsistency of their season.
However, O'Shea believes there is a growing belief within the camp, fostered in large part by full-back Phil Bardsley, who came close to leaving the club during the summer as former manager Paolo Di Canio staged a cull.
The 32-year-old Republic of Ireland international said: "He was inches away from leaving the club. Fingers crossed now we can keep hold of him, because he is the heart and soul of the place as well.
"He has been here the longest, him and Jack [Colback], I think it is, and you need to keep that at the club to build its profile.
"Just for instance, if Catts [Lee Cattermole] and Phil had left, Jack would have been the longest serving player, then it would have been me and Wes (Brown), and that's crazy."
If attention switched swiftly to Saturday's trip to Craven Cottage, Poyet insisted his players should be able to enjoy their triumph for a few days at least after seeing them condemn United to a third successive defeat for the first time since May 2001.
Ryan Giggs' own goal in first-half injury time gave them their lead, but it was cancelled out within seven minutes of the restart when Nemanja Vidic powered home a header from Tom Cleverley's corner.
O'Shea said: "I was frustrated when I let Vida get a little half a yard on me. I know how good he is in the air. He attacked it well, but I should have been able to stay with him better."
However, Sunderland were back in front when, after Cleverley had been adjudged to have tripped substitute Adam Johnson, Fabio Borini sent keeper David de Gea the wrong way from the spot to win it.
Johnson made a major contribution as he repeatedly ran at full-back Patrice Evra, who was on a booking, and O'Shea is hoping for more of the same over the weeks and months ahead.
He said: "If we can keep that player for the rest of the season, he is going to be brilliant for us because you see the quality he has.
"Once he has that confidence as well, he's a magical player and hopefully he can continue that form for us."