Wigan, fresh from a 2-0 defeat by Chelsea at the DW Stadium last weekend, dominated possession and edged into the lead when Franco Di Santo fired past Saints keeper Kelvin Davis in the 51st minute.
Southampton, who were playing their first top-flight game at St Mary’s since being relegated in 2005, managed nine shots on Ali Al-Habsi’s goal, but the visitors held on, with Koné sealing a 2-0 win in the 89th minute.
“I am delighted, as we knew we were coming in the worst possible moment to play them due to their winning momentum from their achievement to get into the Premier League,” Martínez told BBC Sport.
“They put us under massive pressure early on, and from then on we composed ourselves and slowly grew into the game.
“The strikers live on great finishes and scoring goals. They did huge jobs for the team, and they emptied themselves, and the goals were their reward.”
Meanwhile, Nigel Adkins admitted his side were punished for their wastefulness in front of goal, with Southampton now languishing in 18th place.
“The Premier League is a relentless division. We had opportunities and didn’t take them. You have to be ruthless, or the harsh reality is you will be punished,” said Adkins.
“Goals change games, and 1-0 down with 20 minutes to go, you change your formation to get back into it; that is my responsibility. But, the 4-4-2 saw them have far too much of the ball.”
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