Sharp was not in United’s matchday squad due to a calf injury and was left with a bleeding lip.
“It’s cowardly and he was knocked to the ground,” Heckingbottom said.
“He has had stitches and is shaken up. His safety was put at risk at a place of work.
“We have the footage and something will be done about it. Bill was minding his own business off the pitch, trying to get our players away.”
‘FA: “We will be investigating the incident as a matter of urgency”’
It is the second fan attack to have taken place at the City Ground in just over three months after a Leicester City supporter was convicted of assaulting three Forest players during the sides’ FA Cup fourth-round tie there.
Forest were not punished on that occasion but are likely to be sanctioned this time by the FA, which in 2019 fined Birmingham City £42,500 after one of their fans attacked Jack Grealish during their Championship game against Aston Villa.
An FA spokesperson said: “We will be investigating the incident as a matter of urgency and will be working alongside the clubs and the relevant authorities to ensure the appropriate steps are taken.”
Tuesday’s attack occurred as Forest fans invaded the pitch to celebrate their victory over United, which secured their first trip to Wembley in over 30 years. Forest won a dramatic penalty shootout 3-2 following a 3-3 aggregate draw, which precipitated a pitch invasion.
Forest released a statement after the match, which said: “Nottingham Forest Football Club are appalled to learn that our former player, Billy Sharp, was assaulted leaving the pitch after tonight’s match at The City Ground.
“The club will work with the authorities to locate the individual in order they are held to account for their actions, which will include a life ban from Nottingham Forest.
“The club would also like to apologise to Billy personally and to Sheffield United Football Club.”