Byrne's goal ensured the Iron went into the play-offs, where they will face MK Dons over two legs.
"The bookies cleaned up. I think my dad had a couple of quid on it, he rang me in the morning," he told BBC Radio Humberside.
"It's terrific, no one picked me up and Macca [McCann] stuck it right on my head. The rest is history."
United were sluggish in the first-half, and Byrne revealed that a teamtalk from the Iron manager Nigel Adkins had helped the players turn the game around in the second period.
"We didn't do ourselves justice at all. It was important we took stock at half-time, we had time to rectify what we did wrong.
"The gaffer drummed a belief into us at half-time. There was a part of me that thought it was going to slip away, but there's a great belief among the team that we're always going to score."