The Scotsman and former Cardiff head of recruitment Iain Moody are under investigation by the Football Association after a series of text messages were detailed in a dossier reportedly sent to the body by Cardiff owner Vincent Tan.
Mackay, whose impending move to Crystal Palace was called off once the allegations came to light, has apologised for three "inappropriate" texts that he sent during his time in Wales.
However, the 42-year-old has suggested that the "immense pressure" that he was under at Cardiff may have contributed to his controversial remarks.
When asked by Sky Sports News if he accepts that being under pressure is not an excuse, Mackay said: "Yeah, there's absolutely no doubt that there's no acceptability in terms of being under pressure or not under pressure as far as that's concerned.
"I suppose I would humbly ask people to ask themselves the question that if their own mobile phone was taken and every private text was scrutinised, there would be a certain amount of embarrassment there for everyone, but at the same time, it was something that was unacceptable but as far as I'm concerned, I've been in a multicultural football environment for 20 years.
"I love British football and I am no racist. I am no sexist and I'm no homophobe and I'm no anti-Semitic. The people that know me know that, and I understand that it's the people who don't know me that I've got to convince of that."
Moody resigned from his post as sporting director at Crystal Palace earlier this week after the allegations came to light.