The England international was given a "substantial" fine and ordered to undergo diversity awareness training after a video of the incident emerged.
He said he had not realised that the term - "Jap" - is offensive.
Show Racism the Red Card said it was "encouraged" that Vardy had recognised the "huge mistake" he made.
In an excerpt from his autobiography published in The Sun, the footballer said: "The word 'racist' is a permanent stain against my name. It's worse than a criminal record.
"I was angry at the time and I'd had too much to drink but I'd never have used the word 'Jap' if I'd known it was racist."
Writing about the diversity awareness training, Vardy said: "The tutors explained some of the context behind the word and its meaning, dating back to the Second World War.
"It made me feel more embarrassed."
Show Racism the Red Card said many people do not understand that "Jap" - a derogatory term for a Japanese person - is offensive.
"As an anti-racism education charity, it is important that we look at the history of the word used and help people to consider why it is regarded as racist," it said in a statement.
"Jamie Vardy made a mistake; he has recognised it, apologised and undertaken diversity training.
"If people can learn from their mistakes and change their behaviour then not only is it unlikely that they will act in a racist way in the future, but they may also help others to modify their language and behaviour too."
Vardy made the racial slur at Leicester's Grosvenor Casino in July 2015.
After investigating, Leicester opted against sacking him after taking into account his "prompt apology".
He went on to be a key figure in Leicester winning the Premier League title in one of the greatest sporting stories of all time.
Vardy said he has personally apologised to the man involved.
"I needed him to see how sorry I was," he wrote in the book, which is due to be published by Ebury Press.
"I wanted him to know there was ignorance, not malice or prejudice, behind the word I used."
Leicester sacked three players - including the son of former manager Nigel Pearson - in June 2015 after they took part in a racist sex tape filmed on the club's end-of-season tour of Thailand.
Leicester City striker Jamie Vardy has said he was "ignorant" rather than racist when he used a racial slur against a Japanese man in a casino.