Chants referencing the Hillsborough disaster were directed at the travelling Liverpool supporters during the match at Luton's Kenilworth Road.
On Monday the FA confirmed that they are "seeking observations" from Luton as well as "further details" from police.
An official statement from the FA read: "We strongly condemn chanting of this nature and will continue working closely with our stakeholders across the game, including the clubs, leagues, fan groups and the relevant authorities to proactively address this issue."
Former Liverpool defender Jamie Carragher addressed the chants during Sky Sport's live coverage of the match.
"Supporters have got to have rivalry but we are better than that. A lot of clubs have been guilty of that over the years but football fans are better than that," he said.
Luis Diaz snatched a point for Liverpool with an injury-time header, despite currently dealing with the kidnapping of his father in Colombia.