Speaking after the match Martinez said: "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.
"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.
"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."
Next up for the Latics is the visit of Southampton to the DW Stadium on Saturday for a very important fixture at the bottom of the table.