The result completed an unwanted hat-trick of first-round exits for Latics after they fell at the first hurdle in the Carling Cup and Johnstone's Paint Trophy.
Oldham chief executive Alan Hardy said: "The embarrassing defeat at Accrington can only be described as a financial disaster.
"We were hoping for a cup run at least up to the third round which would have brought in valuable revenue in what is proving a financially challenging season."
The scoreline on Saturday flattered the Latics after their League Two opponents raced into a three-goal lead. Only a late rally ensured that the result became respectable as Oldham sought to spare their blushes at the Crown Ground.
Ray Putterill did the damage. The former Liverpool trainee tore the League One side apart with two well-taken goals that sandwiched an assist for Jimmy Ryan to add to his already burgeoning reputation. The youngster has impressed since joining Stanley in the summer and Oldham had no answer to his skilful play.
Dickov had picked a first-choice line-up for the match and was eager to advance to the next round, but his side simply did not turn up in the opening half. His charges did improve after the break and rallied to keep their less illustrious opponents on their toes.
Northern Ireland international Warren Feeney kicked off the fightback as he drilled in a chance with twenty minutes to go. The Accrington defence began to waver and appeared as if it would collapse when Dave Winnard felled Filipe Morais in the area only six minutes later. Dale Stephens was on target from the spot and a one-time unlikely replay looked on the cards.
The out-of-form home side continued to defend desperately and looked to have been breached when Paul Black won a header in injury-time. The defender could only strike the post as Oldham exited at the first round stage of the FA Cup.
The week of Lancashire derbies has been a bad one for Oldham after the postponement of the Rochdale away match last Tuesday. That tie looks set to be played on Saturday 27th November following both team’s giant-killing exits in the FA Cup - though the provisional date is subject to police confirmation.
Disclaimer: The views in this article are that of the writer and may not replicate those of the Professional Footballers' Association.