Over 30 of the bets were on his team to lose.
"Anyone who knows me personally will know that I only ever want a win for my team," Heys said in a lengthy statement on his website (www.robheys.co.uk).
"This has always been the case and on occasions when I have very occasionally bet against my club over the last ten years I would always have been very happy to lose the stake and take the result.
"It is also important to note that I did not make any profit from the bets that have been involved in the FA charges.
"This was displayed in the schedule produced by the FA - in fact on Accrington bets the outcome was a loss of 421 pounds and in respect of the total 735 bets it was an overall loss of 2,318 pounds."
Heys said he intended to appeal the penalty.
Last week Stoke City striker Cameron Jerome was fined 50,000 pounds for breaching betting regulations, while Tottenham Hotspur midfielder Andros Townsend was fined 18,000 pounds earlier this year.
In 2009, four Accrington players and one from Bury were suspended and fined for betting on a match between the two teams, but Heys said his had nothing to do with that case.
($1 = 0.6405 British pounds)
(Writing by Josh Reich; Editing by John O'Brien)
