The Black Cats have dragged themselves six points clear of the Barclays Premier League relegation zone with fine victories over Newcastle and Everton in their last two games after a battling defeat at Chelsea to hand new manager Paolo Di Canio a superb start to his reign.
One more win would take them to 40 points for the campaign and, particularly if it came at struggling Aston Villa on Monday evening, would virtually assure them of a place in next season's top flight.
However, such is the confidence currently flowing through the dressing room that O'Shea believes they can set out to win each of their remaining fixtures.
Asked how many points were still required, the 31-year-old defender said: "We will take another 12, to be honest.
"The next four games, the performances that we have shown, we are confident going into these matches.
"But first and foremost, we took the Chelsea step - we were unlucky we didn't get a point at least; we focussed on Newcastle, we got the three; we focussed on Everton, got the win, and we are just focussing on Villa.
"If we can get something down there, hopefully that should see us across (the line), but we have got two home games then against Stoke and Southampton and a tough away game, so the sooner the better, as they say."
A return of six points from a possible nine for Di Canio has launched the Italian's career on Wearside in remarkable fashion, and has provided an instant return on all the hard work he, his coaching staff and the players have done over the last three weeks or so.
The 44-year-old has been burning the midnight oil at the club's Academy of Light training headquarters, and days off for the players had become a distant memory.
O'Shea and his team-mates were handed a welcome break this week after their successes against Newcastle and Everton, although the Republic of Ireland international had no complaints about the busy schedule which preceded it.
He said: "Look, the lads would have fully taken to it - they might not have been happy deep down inside, but if it meant keeping your place in the Premier League, the lads wouldn't have any days off.
"There's never a problem like that. We are paid to be professional enough like that, that's never going to be an issue.
"The dedication, as the manager stressed after the game, the application the lads have put in and just the focus and concentration...
"It's not that he wants us running everywhere during the training sessions, just for those few little moments he wants us fully-focussed.
"It's so important because the lads see in what the manager prepares, whether it be little videos on the opposition, little things he thinks we can hopefully take advantage of, and when the lads see it happening in games and watch it back on videos, they really buy into what's going on."
Di Canio and his players will return to their video screens this week as they attempt to plot a way past Villa, with their latest evidence Monday night's 3-0 defeat at Manchester United.
O'Shea was watching intently as his former club landed their 20th Premier League title, and he saw enough to know the Midlanders will be no push-over as they attempt to ease their own relegation fears.
He said: "We saw them against United - I don't think many teams would have stopped United in the first half.
"But in the second half, Villa were quite strong and solid and they will be looking to build on that. But we will be looking to continue our run as well."