Heys cited unexpected bills as the reason for the unpaid wages and urged fans to remain calm.
"We have paid some wages at the moment, but we haven't paid them all," he told BBC Radio Lancashire. "Wages were due as of March 1 but fortunately we have managed to sort the funding from the current board."
Stanley, who dropped to the foot of League Two following Tuesday night's 3-0 home defeat to Fleetwood, have regularly battled financial problems since re-entering the Football League in 2006.
Former chairman Ilyas Khan donated around £250,000 to avert a winding up order due to an unpaid tax bill four years ago and he stood down last May after investing more than £2million into the club.
Heys added: "It's tremendously difficult trying to keep a League Two football club going.
"Credit to all the players and staff - to be fair, they've all carried on working. Everyone who works here goes over and above what they've been asked to do.
"It's not acceptable, we're not making excuses, and it's credit to Leam (Richardson, manager) and the players that they haven't used it as an excuse for results not going our way.
"We have got the lowest gates and the smallest wage budget and it is a battle to stay in League Two, but it's where we want to be. We accept that battle because if we wanted an easy life we'd drop down a couple of levels.
"We're fully up to date with HMRC and our usual creditors - it's just a matter of getting these wages paid."