Arsene Wenger's side clung on to a 1-0 victory after Mikel Arteta converted a second-half penalty when Walcott was brought down by Jean Beausejour.
And Martinez insists Wigan should have had a penalty of their own when the ball struck Gunners left-back Kieran Gibbs on the arm in the dying minutes - but referee Jon Moss waved play on.
"The (Arsenal) penalty was very very soft, if anything, I think. Theo Walcott is very clever there," said Martinez.
"It's difficult to tell if there is contact or not, and that doesn't mean it's a penalty, the contact has to stop you from staying on your feet.
"The player's got real experience and he knew a penalty would change the game and give them real hope of the three points and I thought he bought the decision.
"But whether it's a soft penalty or not, the disappointment is then in the other box you've got a clear handball. The ball travels a long distance and the arms are not in a natural position, and that's a penalty.
"And then at the other end if you want to give a penalty where the hands are not in the natural position... I'm really disappointed because the players don't deserve the feeling that they've got now.
"We are in the middle of a period where calls are not going our way and we've got a few players missing.
"I thought we played really really well. We played with a great mentality. The players displayed a big team mentality and I couldn't be prouder."