Lyon conceded he had "made an error" and been held to account by his players regarding remarks made during a session in early April.
As three Indigenous players linked up with the ball at training, Lyon said: "I love the brother boy connection, but we all have to remember we are part of a bigger team here."
Bradley Hill and fellow Indigenous star Nasiah Wanganeen-Milera were among those who took exception to the comment, with Hill contacting Lyon the following day.
Lyon subsequently met with the group and resolved the situation, with the players satisfied their coach had said the wrong thing but had not intended to be racist.
On Thursday, Lyon said there was no formal complaint made to the AFL and rejected suggestions Saints chief executive Carl Dilena should have been brought in to handle the issue at the time.
"It was a really great process driven by the players," Lyon said.
"It talks to our environment in the way it was handled, and the shop floor took care of it.
"If there had have been an impasse and a complaint, it would have been taken outside of that office and escalated.
"Those that are alluding to, 'Why didn't it go to the CEO?', it's because it became a non-issue that was resolved really quickly and appropriately."
Hill and Wanganeen-Milera have shown public support for Lyon since news of the issue was first made public through a Seven Network report on Monday night.
It was reported Lyon offered his resignation at the time of the incident, but the 59-year-old on Thursday moved to clarify that situation.
"All relationships are built on trust ... so the context of that was, 'If you don't think I can rebuild the trust, I would consider my position'," Lyon said.
"It wasn't a 'take it' (offer of resignation) ... so that was the nuance to it. I think that's really important."
The coach said he "hugged it out" with the First Nations players at their meeting.
"I am grateful that we got together. It's a psychologically safe environment, we're all accountable," Lyon said.
"Everyone talks about psychological safety and the ability to be your authentic self, express yourself and your opinion, and be safe about it and be heard - that's what occurred and we're really proud of that."
St Kilda next play Carlton at Marvel Stadium on Saturday night.
