Forest lost the second leg of the semifinals 2-1 after extra time, making it 3-3 on aggregate, but won 3-2 on penalties at the City Ground after three saves by goalkeeper Brice Samba.
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The last save led to a pitch invasion by the home fans to celebrate the win, and video showed one supporter running up to Sheffield United captain Billy Sharp and headbutting him to the ground as he stood watching by the sideline.
Sheffield United manager Paul Heckingbottom called the incident "assault" and pledged that the perpetrator "will be dealt with."
Nottingham Forest issued a statement saying it would work with relevant authorities to locate the perpetrator, who would be banned for life from the club.
"Nottingham Forest Football Club are appalled to learn that our former player, Billy Sharp, was assaulted leaving the pitch," the statement said. "The Club would also like to apologize to Billy personally and to Sheffield United Football Club."
Two-time European champions, Forest were last in the top flight in 1999. The team can return there by beating Huddersfield at Wembley Stadium on May 29 (streaming LIVE, 11:30 a.m. ET, ESPN+) in one of the most lucrative games in world soccer because of the riches on offer in the Premier League through its broadcasting deals and prize money.
Huddersfield were promoted to the Premier League in 2017 after 45 years in the lower league, before getting relegated in 2019.