The Scot was the Owls’ best player in the 1-0 defeat, which was ultimately decided by a controversial early own goal from Tom Lees.
Wednesday assistant manager Jamie Smith, standing in for Darren Moore who didn’t travel with the side due to a positive coronavirus test, said the goal should have been ruled out for not one but two offsides in its build-up.
Speaking after the defeat Bannan described the feeling in the changing room, which after Birmingham City’s late winner against Swansea leaves them seven points shy of the Championship safety places.
“We’re disappointed not to have come away with anything,” he said. “We’ve performed really well against a top team, but we’ve come away with zero points.
“The lads are a bit down obviously, we came here to take all three points and we think we should have left with at least a point so we’re gutted.”
The Owls face Cardiff City at Hillsborough on Monday.
Bannan said: “We’ve got no time to dwell on it, we’ve got eight games left, one on Monday. We’ll take the positives and I think there were loads of positives today. Man for man I think we matched them and were probably the better team today. We’ve got to pick ourselves up.
“I think with this manager and with that group of players, the way we’re going at the minute it looks tough but we’re quietly confident of getting out of this and we can get out of it.
“Next season will be a massive change.”