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 and Carlos Tevez tucked home from the spot.
"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," said Moyes. "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."
City boss Roberto Mancini disagreed with Moyes' verdict on the penalty.
"I am not happy with some decisions," Mancini said. "There were five, six or seven situations that I didn't like. I think the penalty was a penalty. The fourth official was very close with me.
"How it is possible he can see from there what is going on in the box - it is difficult. The referee was there."
Mancini added: "Everton is always a difficult game because they work hard, they defend very well. In the second half we played better, probably deserved to score another goal.
"In the end we are not happy but the season is long and this doesn't change anything. If you don't pay attention you can lose three points and it is sometimes better to take one."
Source: PA
Source: PA