The Owls pulled off a spectacular comeback, clawing back a 4-0 first leg deficit to take the tie to extra-time at Hillsborough.
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The Sheffield Wednesday fans were well up for it from start to finish, and they managed to complete the comeback with the last kick of normal time as Liam Palmer bundled home in the 98th minute of the game.
For Peterborough, it was a disastrous way to end normal time, with Jamie Carragher pointing out the irony of 'Fergie time', as Darren Ferguson's side fell victim to a late, late leveler - a goal that came two minutes after the allocated six of injury time.
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With the scores level at 4-4 on aggregate, the Posh and Sheffield Wednesday grabbed one more each to make it 5-5, before Darren Moore's side secured a spot at Wembley thanks to a penalty shootout win.
Bannan was an inspirational figure in Sheffield Wednesday's fightback, showing the spirit needed to see them move one win away from promotion.
However even he admitted he was scared to run in to Peterborough boss Ferguson, who was clearly unhappy at how his side had thrown victory away.
Speaking on The Sports Breakfast, Bannan said: "I went into the back room to do an interview with the EFL and he was in there and I bumped into him.
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"I got a wee bit scared and didn't know what to say to him and I panicked!
"He was obviously gutted, as you would be after throwing away a 4-0 lead. He obviously wasn't happy but someone had to lose I guess."