Wednesday have been deducted a total of 18 points this season; 12 for entering administration and a further six for financial regulation breaches.
On Friday, the EFL formally confirmed that there would be no further sporting sanctions applied this season.
The Owls have won only one Championship fixture, losing 13 of their 20 games. They are rock bottom and 29 points from safety, with relegation to League One looking a formality.
Bannan, 36, insisted the players must find a way to dig deep to improve their form.
“There’s only so much that you can blame administration for and the points deductions,” he said.
“Now we need to start winning games. We’re not happy with our performances. We need to be a lot better.
“There’s no time for excuses now. We’re looking forward.”
The club were left with a threadbare squad in the summer after Josh Windass and Michael Smith walked away from their contracts. Star players like Djeidi Gassama and Anthony Musaba were sold.
Wednesday will play four games in 10 days over Christmas and resources have been further depleted.
Yan Valery and Sean Fusire have left for the Africa Cup of Nations while injuries have started to build up.
Manager Henrik Pedersen said this week he has only eight “senior players with Championship experience” and has had to utilise the U21 and U18 squads.
“It’s hard,” Bannan said. “That’s why you see some performances are high level and we’re really strong in games and then other games we probably die off a little bit.
“That’s down to the size of the squad and not really being able to make a lot of substitutions.
“We’re asking the same players to churn out minutes after minutes. It catches up.
“But there’s no time for excuses. We know what we signed up for. We just have to keep going and hopefully there’s good news around the corner.”
Wednesday were given special dispensation to sign Liam Cooper and Nathan Redmond as free agents last month to bolster their numbers.
Bannan said “it would be great” if a takeover is completed in time for next month’s transfer window.
“We can get to January and hopefully get a bit more help with players and start to go on a run,” he added.
“If we want to do anything this season we need to start winning games, and we’ve not done that recently.”