Stanley chief executive Rob Heys admitted the Reds had sympathy from various bodies but had no choice but to resign from the Johnstone’s Paint¿Trophy.
Accrington pleaded guilty to a charge of fielding a suspended player in Ray Putterill in their first round clash at Tranmere which Stanley won on penalties.
The Reds were due before a Football League hearing to decide their fate but have now resigned to stop it going further. Tranmere will now take Stanley’s place in the competition, facing Stockport in round two.
"We are disappointed especially as the Football League and Football Association have expressed a lot of sympathy with us over the situation due to the unusual sequence of events," said Heys.
"Other clubs have also been in touch asking what happened and the only thing we can take from it is that we will learn to check and double check the history of our players no matter what they say as even Sunday League games count."
Putterill played for Halewood Town in the Liverpool Combination last season and picked up a 42-day ban beginning on 30 August but played in the Reds victory over Tranmere the day after.
Stanley weren’t aware of the midfielder’s ban and Putterill said he wasn’t either, picked up for foul and abusive behaviour towards a referee.
"We know now that we have to be more stringent," continued Heys. "We thought Ray’s last clubclub was Liverpool FC and it has emerged that this was not the case.
"If we had known Ray had played even at amateur level we could have checked with the relevant FA. We have learnt and hopefully it won’t happen to other clubs. It does always seems to be Accrington, though.
"It is frustrating but technically we have broken the rules of the competition and so must accept the consequences."
He added: "We are more gutted for John Coleman as his team had played so well and got through to the second round. It is one competition where you stand a realistic chance of getting to Wembley and that’s the disappointing thing."
Although they won’t now face a hearing before the Football League, Stanley will still go before the Football Association next Wednesday where they face the charge of fielding an ineligible player.
