Ex-Cardiff manager Mackay has apologised for sending three messages to the club's former head of recruitment Iain Moody, which he admits were "unacceptable" and "inappropriate".
More messages alleged to be of an offensive nature emerged over the weekend - one allegedly racist, about Cardiff's Malaysian owner Vincent Tan, and three of an allegedly sexist and homophobic nature.
The FA have confirmed they are investigating the dossier of messages involving Moody and Mackay sent to them by Cardiff, but they may be unable to sanction either man if the messages are deemed to be private correspondence.
Triesman, FA chairman between 2008 and 2010, believes Mackay should be barred from the game for a season solely on the strength of the three messages he admits sending.
"If it turns out to be three texts then maybe a season [ban], if it's more than that it may be much more," Triesman said. "Assuming that the evidence is stacked up - I can't pre-try it - I think the FA, in the same sense that it can say to players 'here is a period in which you can take no part in playing', could do so with other people in football."
Lord Ouseley, the chairman of anti-discrimination campaign group Kick It Out, believes the case highlights a greater need to address prejudice and bigotry in sport.
He said: "Malky Mackay is probably thinking 'Hey, I'm unlucky, I've got into a situation where all my texts have been forensically examined'. If that happened to every other football manager, senior administrator and other people at top levels of the game then there wouldn't be many people working in football, the game might just collapse. We have to recognise that there is a serious problem about prejudice and bigotry."