The Toffees went ahead through Romelu Lukaku, before goals from Alvaro Negredo and Sergio Aguero fired City ahead.
Then a big call came when Seamus Coleman was adjudged to have shoved Pablo Zabaleta in the box. Aguero took the penalty and the ball cannoned in off goalkeeper Tim Howard to seal the win - but Martinez was not happy.
"Today we started really bright, we wanted to score the first goal - it was important today but we couldn't keep the lead for long enough," Martinez said.
"You don't want to see red cards in games - there were eight yellow cards but I don't think it was that kind of game. It was a very open, fascinating game of football.
"But the game wasn't controlled at all by the referee."
And on the penalty he added: "If that is a penalty, it's an impossible game - it should never have been a penalty.
"I think that it was an emotional decision from the referee.
"He killed a very good game for both sides."