The two-time All-Star made the revelation during a meeting with reporters following Indiana's playoff victory over the Bucks on Tuesday night ... saying the racial slur was hurled at some point in Game 1 of the series in Wisconsin on Sunday.

Haliburton didn't go into detail about how it all went down ... or how his family and the Bucks reacted ... but he did say his brother "has handled that the right way" in the wake of it all.

Haliburton -- who has three brothers -- grew up near Milwaukee in Oshkosh ... so he had several close relatives in attendance for the game. He went on to tell reporters he believes everyone associated with him has "just done a good job of handling this environment."

The Bucks said in a statement the alleged incident was reported to security at the Fiserv Forum ... although they claim the person accused of saying the slur denied the allegation.

"An arena guest services representative reported that during Sunday's game a few guests were not sitting in their correct seats," the Bucks said. "The guest services representative asked the group to move one section over to their correct seats. Then, one of the individuals in the group claimed to the representative that a person sitting in front of him had used a derogatory term toward him. The accused person denied the accusation. The group moved to their correct seats and no further incident was reported."

"We take our fan environment extremely seriously and are committed to providing a safe and secure experience."