No action was taken against Podence by referee Chris Kavanagh after a VAR check cleared the Portuguese, however, Johnson said in a post-match interview that 'some sort of spit came towards my face.'
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The alleged incident occurred after Podence's late equaliser cancelled out Johnson's first-half opener for Forest in a 1-1 draw.
Forest assistant Alan Tate and Wolves counterpart Pablo Sanz, who were both sent off after a touchline melee early in the second half, have also been charged.
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Forest have also been accused of failing to control their players after referee Kavanagh waved away their penalty appeals when Emmanuel Dennis' cross appeared to strike Nelson Semedo on the hand in the opening half.
A statement from the Football Association read: "Various charges have been raised following the Premier League fixture between Nottingham Forest and Wolves on Saturday 1 April.
"Nottingham Forest has been charged after its players surrounded the match official during the 40th minute.
"It is alleged that the club failed to ensure its players conduced themselves in an orderly fashion and/or do not behave in a way which is improper.
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"Both Nottingham Forest and Wolves' assistant managers, Alan Tate and Pablo Sanz, have also been charged.
"It is alleged that their behaviour during the 52nd minute was improper and/or violent.
"Finally, Wolves' Daniel Podence has been charged after the forward allegedly spat on an opposing player during the 90th minute."
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Forest, Tate, Sanz and Podence have until April 12 to respond to their respective charges.