Former Manchester United full-back Bardsley, 27, was pictured in Sunday's newspapers lying in a heap of £50 notes and was omitted from Di Canio's squad for the final-day 1-0 defeat at Tottenham.
Di Canio said of the situation: "I saw the picture on a website and moments later he was out of my squad. How can I play a player that probably is blurry for three, four days after what's happened?
"I want to deliver a very clear message: there is no excuse to behave like he did. They went out because Wigan lost the game and we stay up.
"I could understand it if we had won the Champions League or maybe the FA Cup. We have to respect the dignity of the club, and the fans.
"I thought that at Swindon... arrogant, ignorant footballers because they've not had many chances to stay at the top level. I have to tell you unfortunately I found a worse environment in terms of discipline in this club.
"This is what I've found in the last few weeks so we have to change completely."
He continued: "We have a fantastic, young academy, they have a changing room next to the adults, but if we don't punish this kind of behaviour, we might not be able to talk about a fantastic academy.
"They're not going to sprint down, get the boots and say 'good morning' to everybody. If we don't punish this kind of behaviour, how do they grow up?
"Maybe they will laugh at the picture. Maybe they think it's fantastic; to be like a gangster. But what mentality are we going to deliver?"
Bardsley has featured regularly for Di Canio since the Italian replaced Martin O'Neill as manager and he scored his first goal of the season last week against Southampton.
Di Canio admitted that he is willing to give the player another opportunity to prove himself at the club despite his actions.
"I will think really carefully. Always I give a second chance to the people," he said.
"He is not a kid, he has a family at home. I'm not here to be a priest."
Di Canio revealed earlier this week that he had fined seven players last week for breach of discipline and the Italian also threatened to cut the squad's holiday short unless they played with "dignity" at Tottenham.
Some Sunderland players had planned to go on holiday straight after the Spurs game, which the Black Cats lost 1-0 thanks to Gareth Bale's late winner, but Di Canio will not allow them to go on their annual leave until Tuesday.
"The next few days we will be together," he said. "Previously some people organised during the week to go from London to Hawaii, Miami... They was thinking about organising their bags, four or five of them were talking about going together with their wives and girlfriends. Not possible.
"Today (Sunday) we fly back to Sunderland, our city, as a team. We stay tomorrow (Monday) together for a sponsors event, then they can go on holiday."