Both players, who voluntarily spoke to police after the game, “strenuously deny the charges brought against them”, according to a United statement, which added that the club were "disappointed" to learn that the duo face criminal action.
After Forest’s penalty shootout victory, thousands of Forest fans invaded the pitch and Billy Sharp, the United captain, was attacked by a home supporter who was later jailed for six months.
The invasion was one of a number of similar incidents at the end of last season, with former United goalkeeper Robin Olsen – now of Aston Villa – complaining of being attacked by a Manchester City fan who had run on to the pitch to celebrate his side winning the league title.
Blades boss Paul Heckingbottom called for a “zero tolerance” approach to violence and intimidation aimed at footballers, as would be the case in other sectors, adding that someone “should lose their job” if similar scenes are witnessed at the end of the coming season – which begins for United on August 1, away at Watford.
And a spokesperson for the players' union, the PFA, said: "The PFA has been in contact with Sheffield United management and players since their play off semi-final against Nottingham Forest, which was one of a series of games affected by pitch invasions and serious fan disorder.
"Following these incidents, we immediately wrote to the relevant football authorities on behalf of players, seeking urgent reassurances regarding measures that will be taken to ensure the safety of players at their place of work.
"More widely, the PFA has been working with the police to demonstrate the immediate and longer-term impact of such incidents and provided impact statements highlighting the levels of intimidation and threat felt by players and their families.
"This is an issue which remains a priority area for the PFA."