Stern spoke on Thursday before Game 6 between the Houston Rockets and Los Angeles Lakers and touched on a variety of subjects, but spent considerable time on Cuban's recent behavior.
After the Mavericks' home loss to Denver on Saturday, Cuban said a fan called the Nuggets "thugs" and then Cuban looked at Martin's mother, Lydia Moore, and said, "That includes your son."
The man who made his fortune off an internet venture issued an apology to Moore on his blog, but Stern felt more should be done.
"I thought it was an attempt at an apology in the blog, which is the way Mark communicates," Stern said. "But (players' association director) Billy (Hunter) and I agreed that something more was called for and I called Mark and suggested he reach out, which I'm reliably informed he did."
Stern wasn't sure if the two ever talked.
He considered the events serious, but said he takes full responsibility for the league not taking any action against Cuban.
"I thought it was time to try to make cooler heads prevail and move to something else," Stern said. "Because this is a league that I think takes justifiable pride in its inclusiveness and diversity, and this was not something I felt particularly proud of.
"It's going to cause me to examine a lot of things that I won't go into in the course of the summer in the way we conduct ourselves. But it's a wake-up call to tread carefully and show a lot more respect for each other."
Speaking of respect for each other, there is no word if Stern heard Martin's Cuban-directed tirade as he left the court following Dallas' Game 4 win -- or if any action would be taken against Martin for those comments.
As for replay, Stern talked about his affinity for tennis and how action stops after each point to make sure it's correct. He knows that wouldn't work for the NBA, but wants to see an expansion of the use of replay and is disappointed that the NBA competition committee hasn't been "bolder" on replay.
"I think that as we have continued to take baby steps in this direction, we may be getting closer to a time when at end game, some kind of a challenge may be considered," he said. "I expect to be voted down 30 to nothing."
He refused to expand on what kind of plays could be challenged or when it would be used.
"We want to have a game called the same no matter who is (officiating) it and we want to assure that we get it right," he said. "Against that we struggle with the problem of to get it perfectly right, you get 16 cameras and take four hours to play the game. And we can't do that. We won't do that. So what you've seen is us move slowly to more replay and I think this is a good time to look at it again."