The new-look Owls gave league debuts to seven summer signings in the 0-0 televised draw at Charlton Athletic on Saturday.
Neither side looked likely to score, captain Bannan going close with an unlikely winner late in the game, but after beating two players he dragged his shot wide with his weaker right foot.
At the other end, Charlton twice went close with Albie Morgan shots, while Jayden Stockley should have done better but headed wide.
“We wanted to come and get the three points, but you have to give credit to Charlton,” said Bannan. “They are going to be a good team in the league this year.
“It was a good performance. Up until the final third we were comfortable, passed it well, just lacked that final bit in the final third.
“But we have a lot of new players, it’s a work in progress and I think in the coming weeks we will start to improve.”
Goalkeeper Bailey Peacock-Farrell had little to do all afternoon, while Lewis Wing, Dennis Adeniran, Jaden Brown, Marvin Johnson and Florian Kamberi all showed promise on their league bows, with Jack Hunt – back at Wednesday after three seasons at Bristol City – slotted back in at right-back like he had never been away.
Fellow new faces George Byers and Theo Cordeanu were unused substitutes, while Everton defender Lewis Gibson arrived at the weekend – on a season-long loan – and summer signings Lee Gregory and Olamide Shodipo are also waiting in the wings.
There was enough evidence against Charlton, that Darren Moore’s new charges are settling in well.
And Wednesday could have bagged all three points, had Bannan produced a finish to match his stunning approach work.
“I don’t really shoot with my right foot,” admitted the Scotland international. “Unfortunately for me I missed, I probably should have scored, if it was on left I think I probably would have.
“I am just glad we didn’t lose, it’s a positive start.
“Charlton are a strong physical team, but we showed we can deal with that which is a positive for us.
“At times before, I think we would have probably gone under, and beaten up by teams. We are not physical, but the determination and togetherness was a big part of how we deal with it.”
The Owls lost striker Callum Paterson in the first half, stretchered off after a head injury, but Owls boss Moore said: “Thankfully it’s good news on Patto, he’s up and around and walking around, he’s fine.”
Charlton: MacGillivray, Matthews, Inniss, Famewo, Gunter, Clare, Morgan, Dobson, Jaiyesimi, Stockley, Washington (Clayden 89). Unused substitutes: Pearce, Davison, Watson,Harness, Ghandour, Elerewe.
Sheffield Weds: Peacock-Farrell, J Hunt, Iorfa, Hutchinson, Palmer, Adeniran, Wing, Bannan, Green (Johnson 64), Paterson (Kamberi 16), Brown. Unused substitutes: Byers, Luongo, Dunkley, Corbeanu, Wildsmith.
Referee: W Finnie (Bedfordshire).