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Franco Di Santo's classy strike and a late Arouna Kone effort helped the Latics secure their first points of the season - something that had looked unlikely early on.
Southampton began brightly, and captain Adam Lallana saw an early long-range effort tipped onto the bar by Athletic goalkeeper Ali Al-Habsi.
Jos Hooiveld also hit the bar late on but Wigan made the most of the goalkeeper's saves and Saints' weak-looking defence to rack up their first points of the season.
"I think to say I am pleased would be an understatement," Martinez said.
"I am very, very satisfied because we knew how difficult it would be and I thought the first half an hour showed that.
"When you come to a newly-promoted side like Southampton with an incredible feeling and momentum from the last two season, we knew we would have to cope with that in the first half an hour.
"I don't think the Southampton players should be disappointed at all. I thought they put us in a position where we had to defend and needed Ali Al-Habsi to be at his best.
"But from then on I think we used our experience from last season when we went to [promoted] Swansea at the Liberty Stadium and had a similar experience.
"We started to keep the ball well, we opened up a few good opportunities and then to score two goals from open play away from home is always tremendous.
"That with a clean sheet in the opening home game of Southampton's season is a real achievement that my players deserve a lot of recognition for."
It was the first ever league meeting between Southampton and Wigan, who brought in summer signing Kone in place of Victor Moses after completing his move to Chelsea last night.
The Ivory Coast international did not disappoint in his first start for the club and netted late on, but Martinez was keen to focus on the team performance rather than individuals.
"I think we need to remember today that the performance was one of those where you need everyone, not just the XI that were on the pitch," he said.
"The three subs that came on had clear instructions that they had to pick up the tempo of the game.
"I think it would be unfair to single out one player. I think the whole team took massive responsibility after losing Victor Moses.
"Victor Moses leaves with our blessing. He has done everything he could to help our football club and with that he helped his career.
"He arrived aged 19 and you get really attached to him, but I think this group of players are desperate to fulfil his responsibility and his boots.
"There are a few players that are desperate to take that role and we've obviously got three games in this busy week.
"You're going to see a lot of players given an opportunity to show what we can do and that is a competitive edge we have in this group."
Southampton came into the game buoyed by last weekend's impressive performance at champions Manchester City, who had to come from behind to win 3-2.
However, Saints failed to replicate that performance at St Mary's today as they fell to defeat - much to manager Nigel Adkins' disappointment.
"We were after the three points today," he said. "Obviously we started brightly, we've had some good opportunities.
"The goalkeeper has made some good saves. We've hit the bar on a couple of occasions.
"I think it just highlights how ruthless the Premier League is.
"Wigan haven't really had that many opportunities but they've gone and scored.
"The first goal has gone and changed there complexion of the game and obviously as we're endeavouring to get a goal back I changed the formation to one we were very good at last year.
"But it just highlights that the 4-4-2 allowed Wigan a spell of 10 minutes when they had far too much possession of the football.
"There was a lot of positives to take from it in terms of the opportunities we did create, but ultimately we were looking for the three points today."
