The Capital One Cup finalists booked themselves an FA Cup sixth round berth with a 1-0 victory over Southampton at the Stadium of Light on Saturday to take their tally for the season to a remarkable eighth home win in the two competitions.
However, for all the excitement on Wearside, from where thousands will embark on the journey to Wembley in a fortnight's time, the main focus remains on the fight for top-flight survival.
That process continues on Saturday when Gus Poyet's men make the tough trip to Arsenal, and they face equally difficult rearranged assignments at Manchester City and Liverpool once they manage to squeeze them into a cluttered fixture schedule, although O'Shea is adamant that they can only contemplate one game at a time.
The 32-year-old skipper said: "Without a doubt. That's going to be key because you never know the way the games fall and with the cup run, we could have a couple of games in the league and different situations, so it's a time for cool heads.
"From the manager's point of view, he has dealt with that extremely well so far and it will be the same going forward, I'm sure.
"But the competition amongst the squad is getting fantastic too and the manager is going to be facing some tough choices, which is always good because competition improves everyone all the time and performances have to improve alongside it.
"Winning breeds confidence and we have to take that forward. But first and foremost, we are back in training on Monday and we get back down to the business of Arsenal.
"There's lots to look forward to, they are big important games. But you have to enjoy these moments as a player too."
That assertion was confirmed on Saturday as Sunderland managed to secure victory despite making nine changes to the team Poyet regards as his strongest.
Oscar Ustari took over in goal, Santiago Vergini partnered O'Shea in central defence with Wes Brown suspended, and there was a debut for fellow Argentinian Ignacio Scocco up front.
Asked if he was having to learn Spanish, O'Shea replied with a smile: "No, they are learning Irish."
Poyet had admitted in the run-up to the game that a replay was simply not an option, and it came as something of a surprise when opposite number Mauricio Pochettino also made wholesale changes with only five of the men who had started at Hull in midweek retained.
In the event, it was the Black Cats' understudies who got the better of their opponents in a distinctly ordinary encounter which was settled by a 49th-minute Craig Gardner strike of a quality at odds with much of what surrounded it.
However, Sunderland were grateful for a glaring late miss by England striker Rickie Lambert, who fired over from just three yards after Nathaniel Clyne's cross reared up off the turf.
O'Shea said: "I think the pitch might have helped us out there.
"Look, we should have killed the game off, but to make that many changes and have the quality of play we had at stages in the game was very pleasing to see with some big games coming up."
Southampton headed south perhaps happy to see the back of the Black Cats having played them four times this season and not managed a single victory.
Assistant manager Jesus Perez was unrepentant over Pochettino's team selection, and insisted there was still much to play for over the remaining months of the campaign.
Asked about the club's aims, he said: "To still play well, still win games, help the young players to improve. They have shown they have a massive future this year and for the next seasons.
"This is the target for our club. Our club is growing up, it is moving, so we have to be proud and happy with how our players are doing so far and hopefully in the next games.
"We are not disappointed, we are just a little bit sad to go out of the FA Cup because we tried to move forward. It wasn't possible to go into the next round, but we protect and we support all our squad."