The Conference side bowed out of the competition tonight as Miguel Angel Llera struck the winning spot kick to settle an epic encounter at Aggborough.
"I'm so proud of the players - they were fantastic this evening," Heeley told BBC Sport.
"We took this right to the distance. I wish Scunthorpe the best of luck, but we've been outstanding.
"The players have done this club proud this evening. The club has got massive potential and the sky's the limit for us. I'm a proud man tonight - the players have been superb."
United will now face MK Dons or Chesterfield, whose second-round tie has to be replayed after the latter were found guilty of fielding an ineligible player.