The FA charged Emery with improper behavior following a incident close to the conclusion of that the 1-1 draw on 26 December.
The Spaniard apologised for the episode, which wasn’t included from the officials’ game report.
“I said to them I’m sorry,” Emery said after the game.
“It was not hard but it touched a single supporter.”
Speaking following the game, Emery told reporters he hoped that the apology would be the close of the topic.
“I kicked off the bottle in frustration but maybe perhaps not at the fans, maybe not with this intention. It’s circumstances. I apologised. I expect it’s the conclusion of the matter, yes,” he explained.
Former Manchester United manager Jose Mourinho has been given a one-match ban after being sent off for kicking a water bottle down the touchline during his side’s Premier League game against West Ham in 2016.