Oldham have expressed disappointment at the Football Association's response to a racist message put on social media by their former defender Anthony Gerrard.
The Latics sacked the 32-year-old for gross misconduct during the summer after he posted a racist joke on the Oldham players' WhatsApp group.
Gerrard, who subsequently joined Carlisle on a half-season deal, has been warned by the FA about his future conduct and asked to attend an education course, sanctions Oldham believe are too lenient.
A Latics statement read: "Oldham Athletic Football Club is disappointed with the FA's lenient punishment of the racist behaviour displayed by a former employee during his time at the club.
"Whilst the club welcome football's governing body dealing with this incident, the racist joke relating to the Islamic holy month of Ramadan posted in the Oldham players' WhatsApp group was a serious matter which we believe has not been dealt with appropriately. We think questions must be asked about the conclusion of this investigation.
"In light of the recent, long overdue debate surrounding racism in football, as a club we feel this level of punishment does not do enough to support the hard work that clubs do to stamp racism out of football.
"More must be done to change attitudes not just in football at the top levels, but also lower down the pyramid as well as in society, and the club feel that this so-called punishment does not echo that message."
Gerrard is reportedly in talks about extending his contract at Carlisle after starting all but three league matches this season.
He is yet to comment following the conclusion of the investigation but Carlisle director of football David Holdsworth said on the club website: "This is something which happened at a previous club and, as such, was ongoing when Anthony came to us.
"We've obviously kept an eye on it and we're pleased that it has now been dealt with.
"For us, here at Carlisle United, we have introduced a new Code of Conduct for all players and staff across the club, and everyone is fully aware of their responsibilities when it comes to interacting with fans, or with each other, on social media or in person."