The Latics had to settle for a point at the DW Stadium because of Peter Crouch's second-half equaliser.
Speaking afterwards, Martinez said: "I think we've seen a Stoke with a real strong energetic edge. They're a strong, physical side.
"So they make things really difficult. We got our noses in front and we wanted to take control of the game. We're disappointed with the way we conceded the two goals though.
"I just felt that we needed a two-goal cushion to get the three points."
Stoke almost nicked all three points late on but were denied by a sprawling Ali Al-Habsi.
"You know that you can rely on Ali," added Martinez. "He keeps performing at that level and it doesn't surprise us any more."
Wigan next travel to Manchester United after the international break in two weeks' time.