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Armson, who is a college education examiner by day, guided Brackley to a 4-3 extra-time first-round replay win against Gillingham.
"I left the house to go to work at 6:30am," Armson told BBC Radio Oxford.
"I didn't finish until 4:30pm and then it was straight in the car to the game, eating my dinner out of a plastic pot."
National League North Brackley will travel to League Two Blackpool in the second round.
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Midfielder Armson, 26, was not the only one to juggle his work commitments before the game as striker Steve Diggin was busy surfacing roads in the build-up.
"That's what part-time football is all about," added Armson. "But, once you get to the ground, you just switch off from all of that.
"I thought we got what we deserved. It's brilliant to cause an upset and a great feeling we'll remember for a long, long time."
Brackley Town hat-trick hero James Armson had to change into his kit in his car before causing an FA Cup upset on Wednesday.