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.
"Considering our performance and the result of the game, I don't think we deserved more today," 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 today.
"After having scored five at Reading and seven against Newcastle, when you sum it up today 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 tonight."
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 today, we scored five at Reading, we would score again today.
"A game of that magnitude we had to play today 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."