The Latics scored two fine goals at the Britannia Stadium through James McArthur's clipped finish in the 50th minute and striker Franco Di Santo's volley in the 61st, although it only served as a fightback after the visitors had twice been punished for lapses at the back.
Ryan Shawcross had put Stoke in front in the 23rd minute, slotting in when Jean Beausejour's attempted clearance off a free-kick had struck team-mate James McCarthy and fallen into the Potters captain's path.
Peter Crouch then made it 2-0 in the 48th minute, tucking home the rebound when Ali Al Habsi parried Charlie Adam's shot.
Reflecting on the 2-2 draw - which moved Wigan out of Barclays Premier League relegation zone, up from 19th to 17th, where they are now level on points with 18th-placed Aston Villa - 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 [Tuesday].
"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.
"That is something we need to address, because I do feel we played like a top team in the second half."
Crouch, whose goal was his sixth of the season and first since September, has been linked with a return to his former club QPR as the January transfer window nears its Thursday deadline.
Stoke boss Tony Pulis this evening confirmed he had received an inquiry from his R's counterpart Harry Redknapp about the striker but stressed any potential deals the Potters are involved in over the next 48 hours will have to be right for the Staffordshire outfit if they are to go ahead.
Pulis said: "QPR have enquired about Peter - whether we do it or not, you will have to wait and see."
Asked if the Crouch matter was ongoing, Pulis said: "Yes.
"Harry has rung me up and asked me about the possibility. I have spoken to Peter about it and then it is up to Peter whether he wants to go. Peter is very happy here and he has made that clear.
"The important thing for me is that if he does want to go, it has to be right for us and also we have to make sure we have someone who will come in and do the same job.
"To do all that over two days is going to be ever so difficult."
He added: "It would be nice to freshen a few things up. If we can, we'd like to get a few new faces in, and there are players here who are not playing that maybe could go out and play, but it has to be the right deals.
"If that happens, you only have two days to wait.
"There has been talk about Peter Crouch, about Kenwyne Jones (the Stoke striker linked with Swansea), about (United States and FC Dallas winger) Brek Shea, loads of stuff.
"I will do my business the way I always done it."
Meanwhile, Martinez has revealed his hopes of recruiting Wigan old-boy Paul Scharner, who is currently at German side Hamburg.
"Over the next 48 hours I am hoping to bring one or two players in and Paul is one of them," Martinez said.
"We had the injury to Ivan Ramis, his season is over and we are very short at the back. Antolin Alcaraz is not back yet, so I am trying to bring some cover in at centre-half.
"Paul could be a perfect replacement because he knows the football club and the Premier League.
"He is someone who could fit in at centre-half and with the way we play.
"The fans would welcome him with open arms and it is something that I am hoping to have positive news on over the next 48 hours."