Wigan started in their normal 3-4-3. Martinez didn't have any of his first choice center backs available so dropped James McCarthy back from midfield to play at the center of the back three. David Jones played alongside James McArthur in the center of midfield.
Wenger stuck with the same lineup he used in Monday evening's 5-2 win at Reading. Theo Walcott was employed at center forward while Alex Oxlade-Chamberlain played wide on the right.
The most interesting tactical feature of the game was Wigan's use of their back three. Because Arsenal were in a 4-2-3-1, Wigan had a 3 v. 1 advantage in the center of defense and therefore had two spare center backs. The two man advantage at the back also meant they were short a man in the center of midfield. To even the numbers in the midfield, McCarthy stepped into the midfield in front of the "outside" center backs Boyce and Figueroa and man marked Santi Cazorla. Wigan still had a spare man at center defense- Boyce and Figueroa were 2 v. 1 with Walcott in deeper areas. Wigan's wing backs picked up Arsenal's wide forwards. In effect, defensively Wigan were playing with a back four of Stam, Boyce, Figueroa and Beausejour with McCarthy playing a holding midfield role tracking Cazorla between the seams. Then when Wigan won possession Beausejour and Stam would push high up the pitch from their wing back positions and McCarthy would drop between Figueroa and Boyce to form a back three. This is very similar to the way Barcelona play with McCarthy playing the Sergio Busquets role.
The strategy worked to stifle Cazorla's offensive contribution. He played the pass that led to Walcott being awarded the penalty but aside from that he had a relatively quiet afternoon with McCarthy constantly tracking his movement.
Offensively, Wigan tried to overload Arsenal in wide areas with their wing backs and wide forwards looking to get Arsenal's fullbacks in 1 v. 2 situations. With Arsenal's wide forwards often failing to track Beausejour and Stam defensively, the two Wigan wing backs were often able to get the ball in space on the flanks. However, their delivery from wide areas was poor all afternoon.
Wenger made the game's first substitution on 75 minutes, replacing Podolski with Coquelin. Cazorla moved to the left and Coquelin played in the middle of midfield. I assume Wenger made the substitution to give the Gunners some extra bite in the middle of the pitch but Wigan were mainly threatening from the wings- it was a poor decision from Wenger and one that nearly proved costly. Cazorla is not good at tracking runners defensively and helping his fullbacks. Within minutes of making the change Stam had blown past Cazorla and received the ball in space down the right wing. Again his final delivery was poor but Wenger's decision to move Cazorla to the left nearly cost Arsenal. Finally, in the 90th minute he brought on Koscielny for Cazorla to provide Gibbs with some protection on the left. It was a substitution he should have made immediately when he had taken off Podolski.
That Wigan lost was no fault of Martinez who got his tactics spot on and frustrated Arsenal defensively for large parts of the game while threatening down the wings. However, they lacked the final delivery needed and still could use a center forward that is lethal in front of goal.