With two outs and the score tied in the fourth inning, Albies took an 0-2 fastball that West initially appeared to rule a strikeout for left-hander Clayton Richard by clinching his right fist. West then changed his mind, apparently thinking Albies tipped the ball, which wasn't caught by catcher Raffy Lopez before it hit the dirt.
Green came out to argue the call and was headed back to the dugout when West tossed him. Green then turned back toward the plate and threw his hat in the general direction of West before engaging him in a more spirited argument. West picked up Green's hat and handed it to him.
As he exited the field, Green got the last word with West. He was caught by TV cameras and microphones taunting West over his shoulder as he went down the dugout tunnel: "Don't worry, Joe, I'm leaving, so you can go call another call wrong."
After the game, he addressed the exchange.
"I'm not going to get much into details. ... I think there were some mics on the field," Green said. "I just appreciate him picking up my hat. I've been ejected a lot and never had anyone pick up my hat and hand it to me, so I can appreciate that.
"Don't want to run back through it at this time. I'm just thrilled with the way the team fought tonight."
It was the second straight game in which Green had issues with an umpire's call. He was upset after a video review confirmed Braves catcher Tyler Flowers was hit on the hand by a Tyson Ross pitch in the Braves' 4-2 win on Thursday. Green challenged the call and lost.
After the game, he said, "Flowers said probably five times that he wasn't hit. The replay said he wasn't hit. It's those moments as a manager that you aren't even sure why you have replay. It was blatantly obvious that it didn't hit him."
Green was more brief after Friday's game.
"I think I've said absolutely everything I want to say about umpires," he said.
The Associated Press contributed to this report.