Two strikes from Rob Wolleaston, either side of Daryl Clare's equaliser for Burton, were enough to secure the win for the U's in front of a near capacity crowd at the Trade Recruitment Stadium.
The final whistle was greeted by jubilant scenes with fans spilling out onto the pitch to celebrate their side reaching Wembley for the first time since winning the Division Four play-off final in 1990.
Quinn told BBC Radio Cambridgeshire: "I was delighted to be on the pitch with them at the end to see the smiles on peoples' faces.
"You can see that they haven't had a bit of success for a while and I think every one of them's going to enjoy the day when we go down to Wembley."
The U's will meet Exeter in the Blue Square Premier play-off final on Sunday, 18 May.
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