Two mistakes at the back for the visitors were costly as Southampton cruised to a seventh home Premier League win of the season to open up a three-point advantage over Wenger's men in fourth spot.
Sadio Mane took advantage of a Laurent Koscielny slip after 34 minutes to open the scoring, the forward finishing with a perfectly executed lob over a stranded Wojciech Szczesny.
A mix-up between the goalkeeper and Mathieu Debuchy presented Dusan Tadic with the second goal after 56 minutes, and it could have been worse had the French defender not headed Graziano Pelle's effort off the line shortly after.
Wenger said: "I am disappointed because it was a self-inflicted defeat. We made the mistakes at the back and we were punished.
"Sometimes we look like we can go on a run and then we have a hiccup. We have to learn from that very quickly.
"Today was a game that was winnable and we lost. That's my main concern, the lack of defensive consistency."
Meanwhile, Wenger played down an incident late in the game that saw a fan race into the technical area to confront him.
"There was a young boy, yes," he added. "I think he was a Southampton fan. He was not aggressive at all. I don't think he said anything."
Arsenal's attentions now turn to their defence of the FA Cup, with Hull City waiting for them in the third round on Sunday in a repeat of last season's final.
