The Premier League Clarets were eliminated at the first hurdle by a League Two club from nine miles away in their first ever competitive meeting since Stanley's reforming in 1968.
Matty Pearson's winner in the final stages of extra time was not even greatly received by the majority, though, with 1824 Burnley fans making up the bulk of the 3,170 who had come to watch a fixture that was televised.
It dismayed Coleman on a night when the manager, who has spent the majority of the 21st century with the club during two stints, saw his team land a trip to West Ham in the third round.
"I've been critical of the numbers and I think rightly so," Coleman said.
"This is a once-in-a-lifetime opportunity, it's never happened in anyone's lifetime
You're wondering what everyone wants.
"The chance to cash in a little bit, get a little bit of that back and generate more money towards the playing side, it's been snubbed by the people of Accrington
We can build something special here
"I'm flabbergasted with the gate tonight
The people who've turned their back on us tonight have missed an unbelievable night in Accrington Stanley's history
If you're complaining that you're not coming because of Â£20...I think it's a once-in-a-lifetime opportunity to support your club
We've got to ask ourselves does the town want a Football League club?"
Burnley were brought back down to earth just four days on from their own memorable triumph when they defeated Liverpool 2-0 at Turf Moor
A team featuring 10 changes failed to inspire during the 120 minutes as many of Sean Dyche's fringe players gave little indication they were ready to muscle their way into first-team contention
It may give Dyche further evidence he needs more incomings in this window and he is not restricting himself to a specific area of the field when it comes to transfers
"We're fractionally closer," he said of possible signings
"The desire is all over the pitch for where we think we can strengthen
We can't cherry-pick
We're not in a position to cherry-pick
"We have to work in the market the best we can, find players where we can and if that means shifting our pack then we'll have to do that."
Source : PA