Maynor Figueroa was sent off and Newcastle were awarded a penalty when the Wigan man barged Papiss Cisse inside the area early on.
Demba Ba converted from the spot and then added a second on 21 minutes to leave the visitors facing an uphill struggle but they responded manfully before Gael Bigirimana added some gloss to the scoreline.
"It became a very difficult game in 10 minutes when you give a two-goal cushion and go a man down," Martinez told Sky Sports.
"But I was pleased with was the reaction of the players in the second half. It would have been very easy to feel sorry for ourselves.
"I was extremely proud with the reaction of my players. We gave a real feeling of fear to the Newcastle side. We got on the ball. Unfortunately we couldn't get that early (second-half) goal that you need."
The Latics boss was frustrated by the sending off of Figueroa that turned the game in the home side's favour.
"It was a big decision. You need to be certain of a decision like that," added the Spaniard.
"For me, it was between the two players. I think Maynor Figueroa is allowed to challenge for that ball and we are unfortunate.
"But you're going to get that in football. What I'm pleased with is the way we reacted."
Wigan now face a potential relegation six-pointer against bottom-club QPR on Saturday but Martinez is optimistic despite the scoreline on Monday evening.
He added: "The players are going to get their rewards if they keep doing that. We need to take it into the next home game."