Liversedge won the game 2-1 thanks to a last minute winner, but the match was marred by an alleged incident of racist abuse.
In a statement, Brighouse Town said: "An alleged racial incident took place during the second half of todays game vs Liversedge.
"It was reported to the referee who will be submitting it in his report.
"We as a football club do not accept any form of discrimination and it doesn’t belong in the game.
"Racist language is not welcome at the Yorkshire Payments Stadium.
"The club will form an investigation to find out the culprit and ensure they are banned from the stadium."
In a statement, Liversedge said: "During the second half of our match with Brighouse Town, an alleged incident of racist abuse took place.
"Liversedge FC operates a zero-tolerance policy towards racism and discrimination of any form.
"As a community club, we would hate for supporters or players of any background to feel discriminated against, unwelcome, or uncomfortable at our matches.
"For this reason, we will fully assist Brighouse Town in their investigations."