The incident happened when the Melbourne Stars faced the Melbourne Renegades on January 4 with Stoinis pleading guilty to the Cricket Australia code of conduct level two charge of using personally abusive language and apologising to Richardson.
Ahead of the ODI series in India, Richardson said Stoinis had "looked more angry than I have ever seen" but did not know what had sparked the outburst.
Other than a brief line in the statement after the fine was handed out, Stoinis had not spoken about the incident but addressed it after his record-breaking 147 not out against the Sydney Sixers at the MCG on Sunday.
"There's absolutely no excuses," Stoinis told reporters. "I mean he's a good mate, and he over the last couple of games we've played I think he's wound me up a few times, [but] it's absolutely no excuse to use words like that. And that's what he was trying to do. He was trying to get a reaction out of me and that sort of thing and unfortunately, I took that bait and went too far and that's not acceptable.
"I've spoken to Kane but then even more than that, I think it's not the type of person I am. It's not who I want to be and I understand it's out of line. It's not how I was raised. And I'm not proud of it, but I guess I've just gonna cop that on the chin and, and roll with it now. And also, look, hopefully other people learn from my mistake.
"And unfortunately, that's all we can do. I guess you can't take anything back. You've just got to show it by your actions from going forward."
Richardson said it was normal for Stoinis and him to exchange words when playing against each other. The two have played a lot of cricket together for Australia and were both part of Australia's 2019 World Cup campaign, and have often sparred verbally in domestic cricket. However, Richardson said this was different from what he had experienced in the past.
"We always talk, we're both competitors," Richardson said in Mumbai. "It was just a bit of harmless banter about what was going on on the field and the way he goes about it. I always want to have a chat to him about that. It was just harmless cricket chat. For some reason, he reacted the way he did. You would have to ask him why; it was really out of character. He looked more angry than I have ever seen him. I'm not sure what he was thinking. The learning has to be that it never happens again."
Richardson said Stoinis had contacted him the following morning and while he was not personally offended, he reiterated the words of Australia coach Justin Langer in saying that it was unacceptable for any player to use those words moving forward, particularly as it was the second such incident this season after Australia Test quick James Pattinson was suspended following a similar code of conduct charge in December.
"Yeah, a little WhatsApp the morning after, but not a whole lot of conversation about it," Richardson said. "He realised he made a mistake. I could just tell by his body language for the rest of his innings that night that he knew he made a mistake. I didn't need an apology for myself, he didn't offend me. It's what he said that offended so many people. It was more just his actions and everyone's actions, we can't afford to have that happen again."