The Gunners started 2013 with a whimper on the south coast, rarely threatening in a game the relegation-threatened hosts looked more likely to win.
Gaston Ramirez opened the scoring for Saints after 34 minutes but Guly do Prado's own goal seven minutes later saw Arsenal secure a 1-1 draw.
It was an unusually poor performance from the visitors and Wenger made his disappointment abundantly clear afterwards.
"Considering our performance and the result of the game, I don't think we deserved more," the Arsenal boss said. "It is two points lost if you look at the overall target we had for Christmas. It is frustrating and disappointing as we didn't create a lot.
"After having scored five at Reading and seven against Newcastle, when you sum it up with all the chances we created there is not a lot to consider. Our game lacked purpose, penetration and speed, all qualities we have usually but that we didn't see."
Wenger was clearly irritated by his side's attitude and blamed their mental approach, saying there was a lack of "sharpness".
"It is nothing to do with physical side," he said. "Maybe we thought we scored seven against Newcastle, we thought we would score again, we scored five at Reading, we would score again.
"A game of that magnitude we had to play against a Southampton side that was really highly determined. I felt that we lacked purpose in our game and it was more mental than physical."
- Sports & Recreation