But former Wigan Athletic boss Martinez was left aggrieved by the nature of the defeat and felt that his team should have been awarded a spot-kick of their own in the first half when Matija Nastasic knocked down Lukaku.
On the spot-kick awarded against his side, Martinez told reporters: "I thought it was a football disaster. That should never be a penalty.
"The overall performance of the referee didn’t allow us to compete eye to eye with Manchester City. Unfortunately, he killed the game of two very good sides."I think today the scoreline goes down to big decisions," he told BT Sport. "We didn't get that little bit of luck.
"I thought we started really well, and the one that we had was more of a penalty."
Still, Martinez accepted that Everton's performance had been below-par and lamented his side's inability to take control after seizing the early initiative through Lukaku's fourth goal in three league games.
"We cannot be happy with the way that the goals were awarded," he added.
"We allowed the performance to go, we could have played a lot better, more clever, to concede three goals we are extremely disappointed with that."