The Italian parted ways with the Stadium of Light outfit following a 3-0 defeat against West Brom on September 21, which left the club rooted to the bottom of the table without a league victory this season.
It had been suggested that Di Canio's reign ended due to a backlash from squad members over his management of the team and while O'Shea confirmed those reports, he is keen to move on.
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"Because of the position we're in in the league, we can't keep going back to it. We've got some difficult months ahead.
"Whoever comes in, whether it's Bally [Kevin Ball] or a new manager, we've got tough times ahead.
"We have to stick together and if we keep going back to it, it'll soon be too hard to pull back from where we are."
Caretaker manager Ball saw his team put in a much-improved performance in Sunday's 3-1 home defeat to Liverpool, and O'Shea revealed that the side would welcome the appointment of the 48-year-old on a permanent basis.
He added: "Without a doubt, he's made an impact. If It does happen the players would be very happy. But we will wait and see what the club decides."