Marouane Fellaini put the visitors ahead in the 33rd minute but Carlos Tevez levelled from the penalty spot two minutes before the break.
Referee Lee Probert pointed to the spot after Fellaini appeared to tug Edin Dzeko in the area, although Moyes claimed Leon Osman had been identified as the culprit.
Moyes said: "It's pleasing when you come to the champions and be able to come away with a point.
"But it's no more than we deserved. The way the players played, they played really well in the first half and were compact in the second half to make it hard for Manchester City.
"I'm pleased with a point but in a way disappointed by the goal that was given against us. You come here and sometimes Manchester City their football is terrific and they can score good goals. But I felt the goal they got was really harsh.
"The fourth official said to us it was for a tug on Osman - the ref told him it was for a tug on Osman - well it's certainly not Osman.
"If he has got the player wrong and he says it is for Fellaini, well it's never a penalty kick because if that's what we are going to give then he is going to have to give loads of them.
"So if any team is coming here and they are going to get soft penalties awarded against them, then it is going to be hard to get a result."