Anthony screamed at Garnett as both teams were heading to their Madison Square Garden locker rooms following the Celtics' 102-96 win over the Knicks Monday.
Television footage from Comcast SportsNet New England later showed Anthony waiting outside the Celtics' team bus, apparently in an effort to confront Garnett.
Several police officers and team officials surrounded the superstar center, preventing him from moving toward the bus.
Anthony told reporters Tuesday he just wanted to "talk to KG" and didn't do anything to be suspended, adding he was angered by "trash talk" of a personal nature allegedly hurled at him by Garnett during the contest.
"It's something you just don't say to men, another man," Anthony told the New York Daily News. "I feel like we crossed the line.
"My mindset and motive of going back there to see him at the locker room and seeing him at the bus, I wanted to have a one-on-one conversation with him and talk about it like two grown men," he said.