Puig said about four fans were talking to him throughout his at-bat and continued talking after he hit the homer.
"I reacted that way and stooped to their level," Puig said through a translator. "It happened suddenly. It's something that came out. There's really nothing I can do at this point."
When asked if he expected any monetary punishment from the league, Puig replied: "If they fine me, what's going to happen?"
The homer was Puig's 10th of the season -- all of which have come against right-handers -- and just his second on the road. He has hit double-digit homers in all five of his Major League seasons.
Dodgers manager Dave Roberts said he was unaware of Puig's gesture after the home run.
Ben Weinrib is a reporter for MLB.com based in Cleveland and covered the Dodgers on Tuesday. This story was not subject to the approval of Major League Baseball or its clubs.