The 60-year-old Hassan was sanctioned after blaming refereeing errors for his country's elimination from the tournament in the last 16, while Zico insulted the referee in a post-match interview.
Ibrahim Hassan, Hossam's twin brother and Egypt's national team director, has also been suspended for three matches.
"The decisions include the suspension of Hossam Hassan and Ibrahim Hassan for three matches each, while Ziko has been suspended for five matches," the EFA said in a statement.
The EFA said it had requested the detailed grounds for the decision from FIFA's Disciplinary Committee in order to assess its legal options and determine whether to appeal.
Zico had a goal ruled out for a foul in the build-up, before Egypt's players appealed for a penalty near the end when the score was 2-2.
However, FIFA refereeing chief Pierluigi Collina defended the officiating in the match, saying such allegations could provoke threats against referees and their families.
The suspensions could rule Hossam and Ibrahim Hassan out of Egypt's upcoming matches against Malawi in the next rounds of Africa Cup of Nations qualifying in November, as well as the first match of the March international window. Ziko will be unavailable until June.