Cuco Martina opened the scoring with a curling long-range effort. Shane Long then added the second goal when the Ireland striker fouled Arsenal defender Laurent Koscielny outside the box before getting on the end of Sadio Mane's right-wing cross.
Captain Jose Fonte made it 3-0 with a towering near-post header from a corner in the 55th minute before Long completed the rout in stoppage time.
"We lost too many challenges today, they were sharper than us," manager Wenger told BT Sport after second-placed Arsenal missed a chance to leapfrog Premier League leaders Leicester City.
"We were unlucky as well, their first shot on goal went into the bottom corner from the right back and the second goal came after a foul on Koscielny. I don't take the overall scoreline too much into consideration."
Wenger also described the game as "very, very, very physical" as his Arsenal side remained two points behind Leicester at the top of the table.
"In many challenges we were second best and the referee let a lot go as well," said the Frenchman.
"You have to say 'well done' to Southampton...they fought for their lives and as soon as they scored the first goal you could see it was going to be a difficult game."
Wenger's opposite number Ronald Koeman was delighted with mid-table Southampton's first league victory since they won 1-0 at struggling Sunderland on November 7.
"It was a fantastic performance against a good Arsenal team, that's a big compliment to the players," said Koeman. "We caused them lots of problems up front through Mane and Long, it was a perfect performance.
"Normally I keep criticism of my players inside but sometimes people need to know what the manager is thinking. We showed fantastic belief in everybody and today we showed how good we are if we play at our level.
"The second half was far better than the first, there were some good goals and maybe chances to score more," added Koeman.
Both teams are back in action on Monday as Arsenal entertain promoted Bournemouth and Southampton travel to West Ham United.
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