The Black Cats are through to the final eight of the cup competition after beating Southampton 1-0 on Saturday but are still in the bottom three in the league.
Following the home triumph over the Saints, O'Shea is confident that having the extra pressure of an FA Cup quarter-final - where they await the winner of Monday night's meeting between Brighton and Hull City - will not have a negative effect on their position in the top flight come season's end.
"Without a doubt," said the former Manchester United defender. "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 (Gus Poyet'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 (next weekend).
"There's lots to look forward to, they are big important games. But you have to enjoy these moments as a player too."
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