The Brazilian was frustrated during the 2-2 draw at Anfield after Forest prepared to make three substitutions with the score level at 1-1. Alisson had already been booked for arguing with the referee after the fourth official was not ready with the electronic board.
Forest quickly restarted play while Liverpool were still reorganising. Neco Williams broke into the penalty area before being brought down by Alisson, with Forest awarded a penalty that put the visitors 2-1 ahead.
Liverpool eventually recovered to claim a point, but Alisson's frustration continued after the final whistle.
The 33-year-old walked past the substitution board near the tunnel and kicked it, with footage showing the equipment being damaged.
The FA confirmed that Alisson accepted the charge and received the standard penalty.
"It was alleged that the goalkeeper acted in an improper manner around the tunnel area after the final whistle," an FA spokesperson said.
"Alisson Becker subsequently accepted the charge against him and received the standard penalty."
Liverpool next face Fulham at home on Saturday.
Matias Fernandez-Pardo is edging closer to a first start for Newcastle, although head coach Matthias Jaissle expects to wait until late before deciding if he'll face Leeds on Monday.
Mauricio Pochettino believes Tottenham should be awarded the 2016/17 Premier League title after Chelsea were punished for financial rule breaches linked to the Roman Abramovich era.
Morgan Rogers believes Xabi Alonso has made Chelsea an "exciting" team after the Blues continued their impressive start to the season with a 6-3 victory over Leeds in the League Cup on Wednesday.
Xabi Alonso has moved quickly to dismiss concerns over Levi Colwill's fitness after the Chelsea centre-back was withdrawn during the 6-3 Carabao Cup win over Leeds United.
