The Iranians were one man down in the entire second half and extra time in the knock-out in Canberra on Friday night and Iraq won the penalty shootout 7-6 to gain a semi-finals spot.
Defender Merhdad Pooladi was controversially sent off in the 43rd minute after seemingly stepping over the head of Iraq goalkeeper Jalal Hachim, who was going for a save.
Pooladi dropped to the ground but was sent on his way by Williams who brandished the Iranian's second yellow card of the evening.
Queiroz was furious on the sidelines and could be seen being physically restrained from confronting Williams as he headed in at the halftime interval.
The Portuguese manager has already been fined $3000 for criticising the Australian referee in an earlier match and was holding his tongue when asked about his side's defeat.
"If I make comments today, I finish my career and I don't think after 34 years ... I deserve to finish my career here," Quieroz told reporters after the match.
"You can imagine how I feel, but I cannot express how I feel.
"Because if I do ... tell the truth, what everybody saw in the game, they come and punish me and I finish my career."
Quieroz said Iran clearly had a case against Williams but would leave the judgement to others.
"Can he sleep tonight?
"It's just a question," Quieroz hastily added.
"If it's necessary I put my knees to the ground to show my respect to ask him how can we understand this decision."
However, Iraq's coach Radhi Shenaishil Swadi fired back at Quieroz for putting unnecessary pressure on his men while they were leading in the first half.
"The pressure came from the coaching staff from their bench, which is wrong," Swadi said.
"They were leading one-nil, they should have been more relaxed."
Swadi said Williams was well-known as the "type of referee who loves giving cards and penalties."
But Iran lost focus on the match to its own detriment, he said.
"Iran's concentration after gaining the red card was to put pressure on the fourth official to give a red card or another yellow card to any of the Iraqi players," Swadi said.
"They concentrated on these things, which is wrong.
"The referee gave all the yellow cards in the right situation tonight."
Quieroz also raised doubts about his future with Team Melli, saying he was unsure whether he would stay.
"Sometimes you come to moments in football where you don't know if it makes sense to keep going in this job."
