More than 18,000 tickets for Bristol City's Championship League play-off against Hull City at Wembley sold out within 20 minutes, the club has said.
Bristol City was allocated 36,000 tickets and season ticket holders and foundation members snapped-up 17,400 leaving the remainder up for grabs.
A club spokesman said the levels of sales on Sunday were "unprecedented".
But some callers to the BBC complained of recorded messages and engaged tones when calling for tickets.
Fan Jennifer Blannin from South Gloucestershire said she was "absolutely gutted".
"I was on the phone to the ticket line from 9am this morning," she said.
"The number either rang and rang, was engaged, you got an out-of-order message or an announcement saying there was a high volume of calls.
"Then my brother-in law from the Midlands rang me to say all the tickets had sold out."
A spokesman for Bristol City said: "Clearly some fans have been disappointed and we sympathise with them.
"But even if we had another 10,000 tickets they'd probably have gone as well."
The club said it would be speaking to bosses at Wembley Stadium to see whether it was possible to get a further allocation of tickets.
Following the sell-out a handful of the tickets were appearing on internet auction site eBay for several times the face value.
But Adam Baker from the club added this was illegal and fans should not buy tickets from there or from ticket touts.
Bristol City are due to play Hull City in the Championship League play-off on 24 May.