The Latics added to their shock victory over Manchester United in midweek by beating the Gunners to move five points clear of the Premier League bottom three.
"It is very easy to use the word pride but I am so, so satisfied because that wasn't an accident," said Martinez.
"To play Chelsea, Manchester United and Arsenal in eight days is such a tough task but the manner we coped physically and tactically here should make everyone at the club very proud.
"It was a well-deserved three points and to say that speaks volumes about the performance of my players."
Wigan return to Premier League action against Fulham at Craven Cottage on Saturday.