The Belgian produced a string of outstanding saves to ensure his side remained on level terms, including a brilliant double stop late on to deny Johnny Heitinga and Nikica Jelavic.
While O’Shea concedes the Mackems rode their luck a little, he was full of praise for the Belgian shot stopper.
“Some great defending and a bit of luck and a great save from our keeper has kept us in the cup,” O’Shea told ITV Sport.
Despite seeing his side throw away an early lead in the tie, O’Shea remained adamant he was happy to settle for a replay with the Toffees.
He continued: “You come to a place like Goodison, the run Everton have been on, ok they lost the other night [against Liverpool] but they rested half their team for the game today, so we’re delighted to get them back to the Stadium of Light."
When asked if he thought the tie had now swung in favour of the Black Cats, due to their home advantage, the Irishman insisted the tie is far from over.
“Everton are a fantastic team, we’re under no illusions how difficult it’s going to be. It’s going to be no easy game just because it’s at home,” he added.
Meanwhile, Everton captain Phil Neville was left frustrated with his side’s inability to find a winner but admitted he enjoyed the game as a spectacle.
“With home advantage we wanted to win but it was a great cup to tie to play in," he said.
Neville was one of six players restored to the Everton starting line-up against Sunderland having been rested for the Merseyside derby with Liverpool on Tuesday.
And, whilst the former Manchester United man understood fan frustration in the squad rotation at Anfield, he backed his manager, insisting players need a rest at times.
“It’s a long season you’ve got to play horses for courses," he continued.
“Any criticism that’s levelled our way we take but you’ve got to understand that the demand’s on us.”
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