The U's boss revealed he always had faith in Clarke after the stopper pulled off a crucial penalty shoot-out save to oust the Cherries from the tournament.
Oxford beat their League One opponents 5-3 on spot-kicks as Clarke denied Marc Pugh and right-back Damian Batt converted decisively following a goalless 120 minutes.
Wilder revealed he was confident that Clarke would be the man to help send Oxford into the second round.
He said: "We always fancied Clarkey saving at least one in the shoot-out.
"He's got a fantastic record in saving penalties and he's pulled one out of the hat again.
"We do practise penalties in training. We were always fancying that he would save at least one of them."