The Black Cats closed the gap on safety to one point with Saturday's 2-1 win over Manchester at the Stadium of Light and have 12 games in which to complete another last-gasp escape from the drop.
Traditionally, the Wearside club do well at the business end of the season and after a couple of impressive performances of late, O'Shea is hopeful for a repeat performance this time around.
However, the Irishman concedes it is results which will ultimately decide the club's fate.
"we have a lot more work to do," O'Shea said.
"Ultimately now it’s down to results. We had a fantastic performance against (Manchester) City and got zero points, then against Liverpool were not so good and got one point.
"Then we’d a very good performance against (Manchester) United and got three. We fully deserved the win.
"We have 12 games left, we more than likely need five or six wins, so we know what it’ll take.
"Hopefully it (Sunderland’s latest upturn in form) shows that like the last few years, we’re fighting really hard to stay in the Premier League."
Despite being 19th in the standings with 23 points, 20 of those have arrived during Sam Allardyce's 18-game tenure, which suggests the Black Cats are at least heading in the right direction.
That said, Allardyce's men face a difficult run in, with half of their remaining fixtures against sides in the top 10, including title-chasers Arsenal and Leicester City.