Managerless Wednesday, led by stand-in boss Lee Bullen, are suffering from an injury crisis which a full team pf players all currently unavailable.
Goals by Tom Flanagan, Lloyd Dyer and Tom Naylor secured the win for the Championship's third bottom side, meaning the Brewers had taken four points off Wednesday after their 1-1 draw at the Pirelli Stadium earlier in the season.
This all came after Owls keeper Joe Wildsmith had saved a penalty for the second successive home game after just seven minutes when he denied Lucas Akins.
And Clough said, with so many players missing for Wednesday, his side had to make that count.
"We were fearing the worst and thinking will that (missed penalty) cost us, but I thought credit to Lucas, having missed a penalty so early, his performance after that was exceptional. He did as much as anybody to get us the victory," said the Brewers boss.
"I think we took advantage of Sheffield Wednesday's situation - they have double figures out injured. When you are missing the likes of Barry Bannan and Fletcher and players like that, you have to take advantage."