Romelu Lukaku gave Everton a surprise 16th-minute lead when the Belgian beat City’s offside trap and calmly slotted his third Toffees goal past Joe Hart.
However, Everton’s advantage lasted a matter of minutes as Álvaro Negredo levelled for the home side before Sergio Aguero edged the Citizens ahead before half-time.
Pellegrini’s men, who were thrashed 3-1 by Bayern Munich on Wednesday, sealed three points when Aguero’s spot-kick attempt hit the woodwork before rebounding of Tim Howard’s head into the net.
And Everton manager Martínez felt Lukaku should have been awarded a penalty following a rash Pablo Zabaleta challenge in the first half.
“The score-line comes down to big decisions,” Martinez told BT Sport.
“We didn’t get that little bit of luck. The game wasn’t even for both teams.
“I thought we started really well, scoring the first goal. The goal that we get punished with is very soft.
“Then the one [penalty shout] we have isn’t a penalty. These moments are key.
“The goals are vital. We score the first goal but we concede a little bit too early. But for us, we cannot be happy with the goals that were awarded.”
He added: “Once we got the lead, we allowed the performance to get away from us. I thought we could have played a lot better.
“But because of the decisions and our lack of concentration, we got heavily punished.
“To concede three goals is disappointing.”
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