Gibson was called for two technical fouls in succession and ejected with 10:13 remaining in the fourth quarter by referee Scott Foster.
The Bulls went on to suffer their worst playoff loss in franchise history, 115-78.
"I have a good accord with Scott," Gibson said after the game. "It's one of those games that's chippy; it's playoff basketball, words are going to be said. I don't mean any harm to Scott. He's a good referee sometimes. Just got to keep pushing and move forward.
"I should have ended it a better way, and conducted myself in a better way and just walked away. It's just frustration."
Joakim Noah also was ejected from Game 2, but no fine was announced.