Liverpool were also fined 20,000 pounds and warned as to their future conduct by The FA after their players surrounded referee Kevin Friend who had sent off Jay Spearing in the second half of the match on December 5, which Fulham won 1-0.
Last week Suarez was banned for eight matches and fined 40,000 pounds by The FA for racially abusing Manchester United defender Patrice Evra in October.
He intends to appeal against that decision so was eligible to play in Liverpool's Premier League match against Newcastle United on Friday, but will now miss the game.
In a statement on their official website, The FA said Liverpool were being fined and warned as to their future conduct "for failing to ensure their players conducted themselves in an orderly fashion" during the game at Fulham.
The club admitted the charge, which was in relation to the dismissal of Spearing, but did not accept the standard 20,000-pound penalty for the offence.
However, an Independent Regulatory Commission found Liverpool guilty and the FA imposed the fine on Wednesday when Suarez was also banned after admitting the offence.
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