Iraq, who beat Japan on their way to finishing top of their group, had been in flying form in Qatar and appeared destined to reach the quarter-finals when Aymen Hussein gave them a 2-1 lead in the 76th minute.
Hussein wheeled away celebrating then sitting on the turf pretending to eat - mimicking an earlier celebration from Jordan's Yazan al-Naimat, who scored the opener.
Faghani gave the goal scorer a second yellow card for excessive celebrations.
A 10-man Iraq were left fuming and were unable to hold on against Jordan, who scored in the 95th and 97th minutes to seal a dramatic 3-2 comeback win at Khalifa International Stadium.
"In a big tournament like the Asian Cup you cannot exclude a player after celebrating a goal," Iraq coach Jesus Casas told reporters. Â
"The same happened in the first half with the Jordanian players and the referee didn't take any action.
"The problem was in the timing of this red card. It took place after we had used all our substitutions, so it was a very difficult situation. We didn't have the chance to make any changes inside the pitch."
After the match, Iranian referee Faghani, who has been based in Australia since late 2019 and is listed among Australia's referees for the Asian Cup, was heavily blamed by Iraq fans online for their team's defeat.
This included comments on social media, a petition calling for his suspension as a referee, and the posting of his personal details online.
"The safety and wellbeing of all Football Australia staff and members of the Australian football community is our priority," FA said in a statement.
"Football Australia is in constant contact with Alireza and is providing he and his family with all the support they require.
"Football Australia is also working with e-Safety and relevant law enforcement agencies on this matter."
Highly experienced referee Faghani is officiating at his fourth Asian Cup.
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