League Two Bradford soaked up plenty of pressure from their Premier League hosts over the course of a contest that finished 0-0 after extra-time, the Bantams triumphed 4-2 on penalties - with Latics midfielders Shaun Maloney and Jordi Gomez both failing to convert their spot-kicks.
Martinez was disappointed at the Latics' inability to seal victory in a game he thought they had controlled well.
"I never felt that we lost concentration or allowed Bradford to have a big say in the game," said Martinez, who made nine changes to his first XI from Saturday's league win over West Ham.
"I think we controlled it really well, and we were very unfortunate not to convert any of the chances.
"That was why it was a feeling of frustration more than anything."