The 49-year-old Scotsman was annoyed with that the contentious refereeing decision was the difference between a draw and a win in the 1-1 stalemate with Manchester City
After Marouane Fellaini opened the scoring, the Belgian was later deemed to have brought down Edin Dzeko in the penalty area, with Carlos Tevez duly converting from 12 yards.
Moyes and his players remonstrated with the referee, and the fourth official, Anthony Taylor, angered the manager further by mistakenly believing Leon Osman to be the perpetrator.
The Toffees' boss outright refused to accept the award of the penalty, questioning the competence of the referees and was also keen to point out City's recent fortune with penalties.
"It is not a penalty kick. I don't know how many penalties Manchester City have had in their home games recently, but as far as I know, it is quite a few. They got another one today," he told reporters.
"You can't be giving ones like that. There'd be a penalty every time there's a corner kick. The fourth official told me that it was given for a foul by Leon Osman, so I've got my doubts if the referee saw the incident."
Manchester City manager Roberto Mancini also had his misgivings over the general officiating, but was eager to both show his support for the penalty award and defend the fourth official.
"I am not happy with some decisions; there were five, six or seven situations that I didn't like," he stated.
"I think the penalty was a penalty. The fourth official was very close with me. How is it possible he can see from there what is going on in the box - it is difficult. The referee was there."