The Reds were told last Thursday that McBurnie, whose deadline-day switch was seemingly completed with minutes to spare on August 31, had been rejected by the Football League.
The Leeds-born forward had been training with the club, with Heckingbottom having to break the unfortunate news to him on Thursday afternoon.
Heckingbottom said: “There was an error with paperwork, that’s all I know. I know when I left here at one o’clock on the Friday morning, I thought it was done. And he was in training with us on Thursday.
“It was not nice to ring him on (last) Thursday afternoon. I actually couldn’t get in contact with him when I first found out as he was viewing a house and I think he was close to putting an offer in and signing some papers.
“It was not nice to tell someone who, for a couple of months, had been thinking he had got a chance of playing for us. And he was delighted. For it to not happen, I just feel for him at the minute.”
On the chance of a move being resurrected in January, Heckingbottom added: “Further down the line, I will be looking.
“We have got three strikers and I have always said I wanted four. So further down the line, I will be thinking (of him).”
Heckingbottom will make changes for Tuesday night’s Carabao Cup tie with Derby and is assessing several players who are carrying knocks from the weekend draw at Preston.
Meanwhile, the Reds head coach has revealed that loan midfielder Gary Gardner has spent some time in hospital in Birmingham as a precaution after suffering a reaction to a dead leg sustained on his debut on Deepdale.