Rondo is the starting point guard for the Lakers and Ingram the starting small forward.
NBA executive vice president Kiki VanDeWeghe was in attendance on Saturday and immediately began an investigation into the fight.
James didn't want to dwell on the incident, but rather how the Lakers (0-2) could get better moving forward.
"When you wake up [Sunday], it's a new day," James said. "It's a new opportunity and you leave things in the past and get on with the future."
The Spurs (1-1) are also working a new superstar into their lineup.
DeRozan, a Los Angeles-area native, is already having a positive impact with his new team, scoring 28 points in each of his first two games.
The Spurs played Saturday night at the Portland Trail Blazers and lost 121-108. The Lakers lost 128-119 at Portland in their season opener on Thursday.
San Antonio head coach Gregg Popovich told the Express-News that DeRozan has settled in nicely.
"He's absorbed everything we've given him so far, knowing full well it's a new system," Popovich said. "It will take some time for him to feel totally comfortable, but he's highly intelligent. It's the NBA, it's not rocket science so he's picking it up pretty quickly."
The Lakers won all three meetings against the Spurs last season, their first sweep of San Antonio since the 1997-98 season. The Spurs have lost four in a row to the Lakers altogether.
Ingram missed the final two games against the Spurs last season with injuries, but he scored 26 points in a 93-81 win at Staples Center on Jan. 11. Kyle Kuzma would be a strong candidate to slide into the starting lineup if Ingram is suspended.
Kuzma, one of the team's leading scorers last season at 16.1 points, is off to slow start, shooting 10-for-28 from the floor in the first two games. He shot 45 percent from the floor during his rookie year last season.
Lonzo Ball, a starter at point guard most of last season, would likely move into a starting spot if Rondo is suspended. Ball shot 36 percent from the floor in his rookie year last season. He's 7-for-17 through two games this month.
Hart is averaging 15.5 points and shooting 52 percent from the floor, and McGee is averaging 14.5 points and shooting 70.6.
All in all, James is content with where his team sits after two games.
"Not disappointed at all," he told reporters after the loss to Houston. "Understand that we are going to have some struggles, some early struggles, and nobody said it was going to be easy."