Suarez had admitted the latest charge of improper conduct, and Liverpool have also been fined £20,000 for failing to control their players in the same match—a charge related to the dismissal of midfielder Jay Spearing.
The ruling, announced on Wednesday by the FA, comes little over a week after Suarez was hit with an eight-game suspension for racially abusing Manchester United's Patrice Evra during a match in October.
Suarez had denied the racism allegations and the decision angered Liverpool, who promised to stick by the player and issued a statement in support of the Uruguayan.
Liverpool admitted the improper conduct charge relating to Spearing's dismissal, after a number of players remonstrated with referee Keith Friend.
However, they did not accept the financial penalty for the offence. (For more sports news and updates, follow Ahram Online sports on Twitter: @AO_Sports)