Steve Cotterill said it was “Buxton’s day” after watching his Cheltenham battle back from a goal down twice to eventually avoid an upset and progress with a 6-2 triumph.
Enterprise National League North Buxton led 2-1 at the break, but the Sky Bet League Two side fired in five second-half goals to secure their place in Monday’s third round draw.
Cotterill made a point of acknowledging the travelling fans after the whistle after a sterling effort from the non-league side.
“It’s Buxton’s day and we don’t get any credit for that,” he said. “They had great support and they are a decent team, so it was a really tricky game for us.
“We now want to be drawn against the biggest team we can get, wherever it is. Batten down the hatches, take the money and run home!”
Buxton opened the scoring through former Manchester City prospect Tai Sodje, who capitalised on an error from Scot Bennett before slotting past Joe Day in the 14th minute.
The home side levelled in the 29th minute when Hakeeb Adelakun played in Isaac Hutchinson, who applied a neat finish.
Buxton regained the lead before half-time when George Ward headed Connor Kirby’s free-kick into the bottom corner in the second minute of added time.
Robbie Cundy levelled in the 58th minute before Jordan Thomas’ brace, Isaac Hutchinson’s second and Ethon Archer sealed Cheltenham place in round three.
Buxton boss John McGrath was proud of his team’s efforts despite the final score.
“That’s football for you,” he said. “That’s why we love it and why we hate it, but we keep coming back for more.
“We just fell short of the upset, but I’m massively proud of the boys, they are down and upset.
“This has been a terrific run and made some great memories.
“You might pick up a paper and see 6-2 and think Cheltenham battered Buxton, but it wasn’t like that.”
