O'Shea said that there is a lot of pressure on top-scorer Steven Fletcher, who has scored all five of Sunderland's league goals thus far.
"Fletch has been amazing but there's pressure on us all, including us defenders to pop up at set pieces and score goals," O'Shea told the club's official website.
"I nearly got one on Saturday and we should be with the fantastic delivery we have from the likes of Adam Johnson, James McClean and Seb Larsson.
"We should be scoring more goals from set pieces and that's something we're looking to improve on. Hopefully it will happen because we can't keep expecting Fletch to bang in our goals."
Sunderland are currently 13th in the Premier League with seven points from five games.