The Latics spurned a number of gilt-edged chances with Shaun Maloney, Franco di Santo and Arouna Kone the culprits as Carlos Tevez scored a late winner for an underperforming City at the Etihad Stadium leaving Martinez's side to continue their relegation fight.
"We didn't take the chances, it is as simple as that," he told Sky Sports.
"I thought we were magnificent from start to finish.
"We created four very good chances. I don't think many teams come to the Etihad and create four very good chances in open play.
"Those chances need to finish in the back of the net and that's why we lost the game.
"If we do that in every game, we will get a lot of points. I couldn't be prouder of the performance.
"We limited them to two shots on target, I don't think many teams have done that.
"My players deserve huge credit. The performance is exactly what we need."
The defeat left Wigan in 18th place on the Premier League table, three points from safety with six matches remaining.