Jones, Reform’s only Member of the Senedd (MS), was banned from the Senedd for two weeks last year.
Speaking to Radio Wales Breakfast for the first time since her suspension, the MS for South East Wales said: “I shouldn’t have said those words. I didn’t mean anything by it.”
Asked why she used it, she said: “Growing up around here, when I was young, which is a long time ago now – I’m 46 – language was very different and that was a term used for a takeaway.
“I’m not going to sit here and make excuses because I’m genuinely sorry for that.
“I’ve done language training as my staff, and it will never happen again.
“I’ll be very, very careful of language that I use. I never wanted to hurt anyone and that was never the intention.”
Jones said she had “done a lot with the Chinese community, in the past and since, in Newport… and I’ve had a good relationship with them”.
“I will always be supportive of everybody in this country,” she added.
“I am not a racist by any stretch of the imagination.”