Mignolet was forced to receive treatment on several occasions for knocks but led by example, relishing the physical challenge to secure a second clean sheet of the season.
"Big Simon was fantastic today," O'Shea, who was handed the captaincy on his home debut with Lee Cattermole named on the bench, told safc.com.
"Stoke launch the balls in and batter into the keeper, but he was magnificent.
"The whole back line stood up well. We picked up a few knocks along the way but it was worth it for the clean sheet at the end.
"The save at 2-0 was top-drawer and was a key moment of the game."