The Latics looked down and out when goals from Ryan Shawcross and Peter Crouch put the Potters in charge.
But they scored two fine goals, the first from James McArthur on 50 and the second from striker Franco Di Santo on 61 to secure a battling point.
The point moves Wigan out of the relegation zone, up from 19th to 17th, where they are now level on points with 18th-placed Aston Villa, but above them on goal difference.
Martinez said: "I feel we went into half-time with Stoke having too much to show for it (their efforts).
"The goal was from a free-kick where we were very unfortunate - we don't clear it, it hits James McCarthy on the back of his head and we are 1-0 down. That was the only shot on target they had.
"Then in the second half I thought we grew into the game and controlled it.
"One counter-attack gave them a two-goal lead and I don't think there are many teams at the Britannia Stadium that would be able to come back from that.
"But from that point on, you look at the way we kept the ball and the way we kept showing that character.
"There was a two-goal deficit but we kept playing the same way and you never saw a player losing their composure.
"We scored two goals which were as good as you are going to see in this league from open play, which was very difficult to do against this Stoke side.
"Then we restricted Stoke to no corners. That is down to the hard work of the players and at the end, if I'm honest with you, I think the players were very disappointed that we dropped two points today.
"But it is something we need to improve a little bit more - you can't be that dominant in the second half but concede two goals."