Everton went down to Yaya Toure's first-half penalty on Saturday and Martinez was disappointed with the award of the spot-kick, as well as two other decisions he felt went against his side.
Marriner pointed to the spot after James Milner had gone down under a challenge from Phil Jagielka, a ruling that Martinez disagreed with.
"The penalty decision shocked us and took the confidence out of our game," he told Sky Sports.
"I must admit I'm very disappointed with the assessment of the penalty.
"Phil Jagielka cannot disappear. It's not Phil Jagielka trying to get James Milner fouled, and if you look at the reaction of James he's trying to get up and fight for the ball.
"It's not a penalty in a million years. Sometimes we get carried away by giving it for any sort of contact."
Martinez also had questions over fouls by Eliaquim Mangala and Fernando on Samuel Eto'o and Gareth Barry respectively.
Mangala caught Eto'o in the back with his studs while attacking a corner, before Fernando's high boot made contact with the head of former City man Barry.
Both men received cautions for their transgressions, but Martinez felt both could have been more heavily punished.
"I'm very, very disappointed. The first one is no doubt," he said.
"The contact is horrific, that's a violent action and that wasn't a natural position to justify that angle.
"That should have been given a red card. Fernando's is a high boot, dangerous play, but what we are feeling harshly done by is that three big calls went against us."
