The Latics were close to securing a crucial point in their battle against relegation but Carlos Tevez fired in a late winner to leave Wigan three points off safety in 18th.
Martinez told BBC Sport: "It's very hard to take. At another moment of the season I would be extremely happy. It was a magnificent performance.
"We were the better side and limited City to two shots on target and with the chances we had, it's hard to explain how we didn't get the points.
"It's a performance to be proud of and when you play against a team like Manchester City you have to accept a goal with that piece of magic, but from a football - and tactical point of view - we were better in every department and deserved the points."
Wigan will look to bounce back with a victory when they travel to London to face West Ham United this weekend.