Sharp was left needing stitches after being headbutted by a pitch invader, as Forest fans streamed out of the stands to celebrate their penalty shoot out victory over the visitors from Bramall Lane.
The United captain, who missed the game through injury, received medical treatment in the dressing room afterwards - as club officials began collecting footage of the incident from media companies who were broadcasting the fixture live.
The unprovoked assault happened as Sharp, a former Forest player, was preparing to console his team mates following the final whistle.
“You watch every Monday night football, Sunday afternoons, whatever and there’s always things getting thrown on and invasions,” a visibly angered Heckingbottom said afterwards. “Everyone talks about the safety of the players and nothing has ever been done about it.
“Bill is there minding his own business, trying to get his mates off the pitch. He’s been assaulted, blindsided in a cowardly way.
“He’s been knocked to the ground, shaken up. He’s had stitches. People should have safety at their place of work. We’re getting the footage, we’ve got it and something will be done about it.”
United are expected to liaise with the police when they begin their investigation into the matter.
“It’s a prison sentence waiting to happen,” Heckingbottom added, before Forest issued a statement saying they were "appalled" by the attack. “We’ve got the footage and we’ll be passing it on.
"It's been sorted here (at the ground), it's getting done here."
Trailing 2-1 from the first leg, United produced what Heckingbottom later described as a “heroic” fightback after falling further behind when Brennan Johnson scored early on. But goals from Morgan Gibbs-White and John Fleck sent the tie into extra-time, with Forest goalkeeper Brice Samba producing a fine reaction save to deny Iliman Ndiaye towards the end of the second period.
United missed their first two spot-kicks, taken by Oliver Norwood and Conor Hourihane, before Joe Lolley later skied over for Forest. But Gibbs-White, United’s most influential performer, failed to convert meaning Steve Cooper’s side progressed to Wembley where they will face Huddersfield Town.
“I’m proud of them,” Heckingbottom said. “Even at half time, I thought we would go through. It’s not sunk in yet. I still feel as if we are on that rollercoaster. It will probably sink in over the next few days.”
“I thought the boys gave it everything, absolutely everything,” he added. “They went out on their shield but that doesn’t make it any easier to take, does it. I don’t want to be disrespectful to Forest and I won’t be, so massive congratulations to them.
“I thought we had the better players though, and I wanted us to show that. I’m proud of them, that’s my overriding feeling. Very proud of the lads. But yes, of course it hurts.”