Mikel Arteta's 60th minute spot-kick, given after Jean Beausejour was adjudged to have felled Walcott, proved the decisive moment in a very tight game played in sodden conditions.
It was certainly a clumsy challenge and referee Jon Moss ruled there had been sufficient contact, while the official made himself even more unpopular with the hosts when he turned down a handball shout in injury time.
Substitute Jordi Gomez's shot certainly struck Kieran Gibbs' arm, and Martinez felt it was a clear case of his side being on the wrong end of two decisions.
He said of the penalty: "When I saw it live it looked very, very soft because 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.
"It's disappointing you don't see that consistency. But I think it would be very unfair just to talk about those two incidents.
"When you play against Arsenal and they're running the clock down in the second half and making substitutions to try to cope with the threat we had, it's a real compliment.
"You're not going to see many teams having more possession than Arsenal and I think my players deserve an incredible amount of credit.
"We didn't get any luck and sometimes in football it's better to be lucky than good but I'm very proud and if we can carry on with this level over the next few games we'll get the rewards we deserve."
Ali Al Habsi, playing his 100th game for Wigan, produced early saves to deny Alex Oxlade-Chamberlain and Lukas Podolski but Wigan had the best chance to open the scoring in the first half when Arouna Kone was played clean through but shot wide.
Al Habsi then denied Walcott at the start of the second half while Wojciech Szczesny produced late saves to deny Maynor Figueroa and Kone before the handball controversy.
Arsenal manager Arsene Wenger did not see that incident but was pleased his players showed they could grind out a victory on the back of Monday's thumping 5-2 win at Reading.
He said: "They organised to stop us playing and they did that very well, especially in the middle of the park. We didn't find the same fluency going forward and it was much more a win because we wanted the result than because we dominated the game."
It earned Arsenal a third successive Barclays Premier League victory for the first time since March.
"It's good but it's not enough, you want more," said the Frenchman.
"I hope that gives us a bit more belief and confidence. We have a week to prepare for the next game and hopefully at home we can continue to win our games. It's an important part of the season now."
Walcott was again given his chance up front after impressing in the role against Reading, and Wenger gave the England man qualified praise.
He said: "I wouldn't like to judge him on one game but he has the ingredients to play there. He didn't have much service today, he was a bit isolated but he can always be decisive. Today again he made the decision and he got the penalty."
Wigan were again without seven players through injury but they will be bolstered next month by the arrival of midfielder Roger Espinoza from Sporting Kansas City while they are also close to completing a loan deal for Manchester United striker Angelo Henriquez.
The 18-year-old Chile international has already trained with Wigan and Martinez believes he can bring a much-needed cutting edge up front.
The Latics boss said: "Angelo Henriquez is a goal scorer. He's going to be a top player, he's an out-and-out finisher and he can bring us goals.
"He comes in straight away to a very familiar dressing room with (Chile team-mate) Jean Beausejour and we're very excited to see Angelo developing as a player and help him to get to where he deserves to be, which is competing for a place at Manchester United."