James was denied a foul by Jayson Tatum when driving for the basket with the scores level at 105-105 and 4.1 seconds left in regulation time.
Officiating crew chief Eric Lewis later said his team had "missed the play."
James scored a game-high 41 points in the defeat.
"I don't understand it," he said on the foul by Tatum not being given in his side's favour.
"You've seen some of the games we've lost with late-game missed calls. I don't see it happening to nobody else."
James took his tally to 38,271 career points and is 116 away from Kareem Abdul-Jabbar's all-time scoring record.
"As much as you try not to put it on officiating, it's becoming increasingly difficult," said LA Lakers coach Darvin Ham.
"The best player in the NBA can't get a call. It's amazing."
James' team-mate Anthony Davis added: "I guarantee you nothing's going to happen to the ref. We got cheated. It's a blatant foul. The refs were bad tonight."
Lewis, speaking after the game, said: "There was contact. At the time, during the game, we did not see a foul."
Elsewhere, Joel Embiid registered 47 points and 18 rebounds as the Philadelphia 76ers emerged with a 126-119 win against Nikola Jokic and the Denver Nuggets.
It was a seventh straight win for the Sixers and a ninth game this season in which Embiid has scored at least 40 points.
The Brooklyn Nets beat the New York Knicks 122-115 to secure a ninth win in a row over their rivals.