The Easter Road boss was shown a red card by match referee Kevin Clancy after he booted a water bottle and hit an assistant referee in the aftermath of Celtic's equalising goal.
Although Clancy had initially allowed play to continue as Celtic winger James Forrest lay on the turf following a Tom James challenge, he halted play on the advice of fourth official Nick Walsh and awarded Celtic the free-kick which led to the equaliser.
Heckingbottom was sent to the stand for his furious reaction but insisted it was unclear to his players what was going on with some of them believing there would be a drop ball to restart play.
The Yorkshireman was shown a straight red card under new rules, and compliance officer Clare Whyte is expected to review footage of the incident.
Depending on her view, Heckingbottom could then receive a notice of complaint.