Luton were also given a two-year action plan by an independent Regulatory Commission to help improve fan behaviour.
"Luton admitted that they failed to ensure their spectators and/or supporters conduct themselves in an orderly fashion," the FA statement said.
The club issued a statement saying they accepted the decision.
"As an inclusive, family-oriented club, Luton Town abhors abusive chanting such as this and has a zero-tolerance policy towards discrimination of all kinds," the statement said.
"Those involved were committing a criminal offence and anyone subsequently identified will be issued with a club ban and face potential police investigation."
Luton are 17th in the standings with six points after 12 matches.
The team lost the match against Brighton 4-1 on August 12th.