Anthony confronted Murphy midway through the fourth quarter of the 76ers' 105-87 win over the Lakers. Anthony said the verbal altercation occurred because Murphy repeatedly referred to him as "boy."
The fan was ejected from Thursday night's contest after the incident caused game action to pause for several minutes while the on-court referees attempted to defuse the situation.
In the 24 hours since the conclusion of the game, an investigation found that Murphy -- who isn't a season-ticket holder -- was a repeat offender of the 76ers' fan code of conduct, according to ESPN. He had been warned and disciplined for those previous offenses.
"Some things were said," Anthony told reporters after Thursday's matchup. "Unacceptable. I'm cool with fans heckling, fans talking trash, cheering for their team, booing the other team, I'm all for that.
"But when you cross certain lines, as a man, you just, that's what you're going to see. That's what you're going to get, as you saw there."
Anthony has averaged 13.3 points and 4.1 rebounds across 46 games (three starts) this season, his first with the Lakers.