The Football Association is investigating an allegation of homophobic abuse directed towards a Forest Green player during their League Two match against Tranmere.
Rovers said they were disappointed to learn of the accusation, which Tranmere said is "strongly denied" by the player in question.
The FA is aware of the incident, which is said to have taken place during Forest Green's 2-1 win on Saturday, and is looking into it.
"Forest Green Rovers are disappointed to hear of alleged homophobic abuse aimed at one of our players during Saturday's game with Tranmere Rovers," said a club statement.
"With football clubs and organisations switching off social media accounts in a collective protest against online abuse by fans, it was especially disappointing to have this occur on the pitch.
"We need better from players if we are to expect better from fans. To ensure there is no place in football for abuse of any kind – that has to start on the pitch.
"The club will fully support the FA investigation into this matter."
Tranmere, who said the accused player rejected the allegations, are awaiting the outcome of the FA probe.
A club statement read: "Tranmere Rovers Football Club are aware of the allegation made against one of our players by an opposition player during last weekend's match at Forest Green Rovers. The allegation is strongly denied by the player in question.
"Whilst the club has a zero-tolerance policy to any form of homophobic abuse, given the strong denial of the incident we will await the outcome of any FA investigation before commenting further."
