The Toffees were leading the Barclays Premier League champions at the Etihad Stadium through Marouane Fellaini when the Belgian was penalised after tangling with Edin Dzeko just before half-time.
Everton protested about the decision, feeling Dzeko went to ground too easily, and Moyes was still complaining to the fourth official as the players left the field at the break.
Carlos Tevez was not affected by the commotion as he converted from the spot to cancel out Fellaini's headed opener.
Moyes said: "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.
"You can't be giving ones like that. There'd be a penalty every time there's a corner kick."
Moyes' complaints to fourth official Anthony Taylor also seemed to be exacerbated by a case of mistaken identity.
The Scot said: "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.
"But even if it was Fellaini, it's not a penalty kick, nowhere near.
"They say it levels itself out. We'll see."