Matt Derbyshire’s 21st-minute close-range strike condemned the Owls to their first Hillsborough loss in over six months. It was only the second time Carlos Carvalhal’s side have lost on their own turf all season.
Defeat means Wednesday have fired blanks in three out of their last four Championship tussles and leaves them 12 points adrift of the automatic promotion placings.
Bannan tweeted: “Not good enough one bit today from us, not like us, apologies to the fans but we will be back and go again on Tuesday.”
Having been outplayed in the first half, the Owls dominated proceedings after the break but just lacked a cutting edge in the final third.
Carvalhal said: “It was frustrating we didn’t score of course. We expected to win the game; we prepared to win and it’s a game that was a little strange for us.
“I am disappointed with the result but I am proud of my players.
“From the first to last second, my players fought to try and win the game and 85 per cent of the time we played in the opposition half.
“This is a hard competition. Other teams, not just us, will lose games against teams they are expected to beat.”