Bardsley seemed set to leave Sunderland after finding himself frozen out at the Stadium of Light under Paolo Di Canio.
The full-back was fined and suspended after mocking the opening day defeat to Fulham on the opening day of the season, but Poyet has given the former Manchester United man a reprieve by recalling him to the squad for his first game in charge at Swansea.
Poyet has called on the Sunderland fans to give Bardsley, who has recovered from a broken foot, the chance to redeem himself as he has been impressed by the player's attitude since taking over from Di Canio.
"Maybe he got lucky that there was a change of manager," said Poyet. "Sometimes you know how it works, there is a decision in one part of the club, but then there's somebody else so he got lucky. Now it's up to him to take his chance.
"I appeal to the people, please give him another chance. He told me he knows it wasn't right what he did, and now he gets a chance, so it's up to him. Now I ask the supporters to let him have another chance.
"Let's see how he behaves and what he does. If he makes another mistake, then he's put himself in a very difficult position.
"Right now, I think he can help us. He's a proper full-back, he can play both sides and he can be important for us. I'm going to give him another chance.
"His attitude has been spectacular since I've come in. He's seen an opportunity and he's put himself in place to take it.
"I saw him on the first day and he was already coming back, fitness-wise. Then when a player comes and asks you to play football and asks to be part of the squad, that means he knows what he's done, and he's willing to help the future of this club.
"I'm not going to put him on a scale to compare him with everyone else, but he's up there with the best."
Poyet takes charge of rock-bottom Sunderland for the first time at Swansea on Saturday insisting he is eager to turn on the style - but only once Premier League survival is assured.
Poyet's attacking philosophy won plenty of plaudits in his previous job at Brighton but he has urged Black Cats fans to be patient as he sets about moulding a struggling team in his own image.
Poyet added: "When you pay for a ticket as a fan you want to see something special and you want to be proud of your team. There is no better feeling than going back to your friends and talking about one great move or shot or save.
"For that you need quality and an identity and I'm sure we are going to have great times here, but it's a process. The priority is to win.
"The sooner we start winning the easier it is for the players to relax and understand the way we want to play."