"Everybody wrote us off. Everybody told us we couldn't do it but it's unbelievable."
The Owls had lost the first leg 4-0 and been booed off the pitch by their fans after a chastening night in Cambridgeshire last Friday.
However, they stormed back at Hillsborough to win 5-1 on the night after extra time for an aggregate score of 5-5. That sent the tie to penalties - and they prevailed 5-3 from the spot.
Prior to Thursday, no team in the English Football League play-offs had ever overcome a first-leg deficit of more than two goals.
Owls inspired by previous comebacks
Captain Barry Bannan was one of five Sheffield Wednesday players to score in the shootoutBannan said that Wednesday had been buoyed by watching previous great comebacks in the days leading up to the game.
"We've watched comebacks all week from the big teams in the Champions League," he told Sky Sports.
"It was all about believing. When we have the fans behind us, anything is possible.
"It's the best game I've ever played in. I'm so happy because all these lads deserve it. I give everything for this club to get us promoted. Everybody wrote us off but we showed we're made of strong stuff. We're only halfway there.
"Those who were booing us last week, saying we're not fit to wear the shirt, have a look at this."
Goalkeeper Cameron Dawson, who had endured a miserable night in the first leg, echoed Bannan's sentiments on the belief the players had gone into the second leg with.
"It was building blocks, really," he said. "We came in the day after the first leg and that was tough. We had some honest conversations.
"Credit to the staff. Every day they've built on those building blocks and given us more belief as the week's gone by."
Wednesday published a statement earlier in the week to condemn a racist post directed at boss Darren Moore on social media in the aftermath of the defeat at Peterborough.
Bannan, who has been with the Owls since 2015, said the comeback was for the 49-year-old.
"What he [Darren Moore] has done is unbelievable, to turn around the mindset of the players," he said. "I'm so proud of him how he's handled this week after the racism he's experienced.
"That one's for him."
'This is the greatest comeback I have ever seen'
Lee Gregory's spectacular overhead kick, brilliantly saved by Posh goalkeeper Will Norris, was one of the Owls' 28 shotsFormer Owls boss Brian Laws was commentating on the game for BBC Radio Sheffield and said the turnaround had left him "speechless".
"I've never seen anything like this," he said.
"What an incredible evening I have seen unfold. My thoughts immediately go to Darren Moore, who has gone through the mill with criticism after the first game.
"It was so nasty and vicious, but his professionalism, his calm and cool, has allowed his team to do something so remarkable.
"My heart goes out to him. I want to congratulate him."
Former Sheffield Wednesday and Crystal Palace striker Clinton Morrison, who was there for Sky Sports, said it was "the greatest comeback I have ever seen".
On the other side, former Peterborough striker Francis Green wondered whether Posh boss Darren Ferguson's decision to tighten up defensively when the side trailed 2-0 at the break had ultimately been decisive in handing Wednesday more momentum.
"Peterborough made two substitutions at half-time, bringing on two centre-backs. I understood why Darren Ferguson did it, because Wednesday were bombarding the wide channels," he told BBC Radio Cambridgeshire.
"As a player, I used to love psychologically when the other team made negative substitutions. It showed me the opposition were scared of my team.
"They were still in control of the tie at half-time, but they had no outlet. They had no way of attacking Wednesday.
"You bring criticism on you when you do that."
Moore left to enjoy sweet success
Sheffield Wednesday boss Moore said his side's effort "had not sunk in yet".
The manager revealed he had shown the team all 49 of the goals they had scored across their home games in League One this season to inspire them.
"I'm really pleased for everyone connected to the club. We have shown what can be achieved when you stick together," he told BBC Radio Sheffield.
"After the first leg, we got back to Hillsborough at half past one in the morning and I didn't go to bed until seven and then came back here at 11 to go through the game.
"We worked on the mindset and had some really good detail in training, we worked on penalties every day."
He added: "We were actually ahead on what we wanted when we went 2-0 up and the crowd was into it then.
"I've never seen anything like it. To score at the end and keep going was magic for me."
The former West Brom and Doncaster boss said he would celebrate his side's remarkable success with some sweets.
The biggest but is it the best?
There is no questioning the extraordinary scale of Wednesday's comeback. But was it the best play-off match ever?
BBC Sport conducted a poll three years ago to ask fans for their most memorable play-off moment from a selected shortlist of 10.
The top three were Derby's 4-2 win at Leeds in 2019, Troy Deeney's last-minute winner for Watford against Leicester in 2013 and Charlton's victory over Sunderland on penalties in the 1998 Division One final after the match had finished 4-4.
Whether this one tops the lot is probably down to which team you support - but as Moore acknowledged "they'll be showing this one for years to come".