Neither James nor his manager, Maverick Carter, cited specifics when talking to CNN for a story that aired Wednesday night.
James did not want to spend much time on the subject after Thursday's Heat practice.
"I think people are looking too far into it," James said. "But at the same time, sometimes it does play a part in it. I've said what I had to say, and I'll continue to move on."
In the interview, CNN correspondent Soledad O'Brien asked about "The Decision," the one-hour special on ESPN in which James announced that he would play for the Heat, and some of the negative headlines it generated.
"It's just about control and not doing it the way it's always been done or not looking the way that it always looks," Carter said.
O'Brien asked if race played a role.
"I think so at times," James said. "It's always, you know, a race factor."
Said Carter: "It definitely played a role in some of the stuff coming out of the media, things that were written for sure."
James turned down a chance to stay with the Cleveland Cavaliers and ultimately decided to join the Heat in the oft-criticized televised special that raised $3 million for the Boys & Girls Clubs of America.
It's not the first time race has been a discussion point in the aftermath of "The Decision."
After James made his announcement July 8, Cavaliers owner Dan Gilbert responded that same evening by releasing a fiery letter to fans of his team, saying James was being "narcissistic" and "cowardly." That prompted Rev. Jesse Jackson to enter the fray, saying the Cavs owner saw James as a "runaway slave."
An e-mail to Carter's representative requesting further comment was not immediately answered.
"I don't walk in LeBron's shoes," Heat coach Erik Spoelstra said. "From our standpoint, we've moved on from the summer."
Information from The Associated Press was used in this report.