Owls striker Tudgay apologised for a performance manager Brian Laws described as "a shambles", but was unable to account for Wednesday's chronic inconsistency this season.
Tudgay told the Sheffield Star: "To the fans, we apologise. We showed them nothing. They spent money to go to the game and were robbed in a way.
"It's crazy. We've played well before but then we put in a poor performance like that. It's certainly not a lack of togetherness, we're as a strong as ever in that respect.
"We just didn't turn up. We let ourselves down. We've let Sheffield Wednesday down and the fans and what we now need to do is to give them a better day at Bristol City on Saturday."