Gaston Ramirez opened the scoring for Saints while the Gunners levelled matters shortly before half-time when Guly turned Theo Walcott's free-kick into his own net.
This result and performance was in sharp contrast to Arsenal's 7-3 triumph over Newcastle three days ago.
The hosts more than held their own, particularly in the second half, and Wenger was frank in his assessment.
He said: "We were not very good offensively, we didn't create enough.
"Defensively, we were not too many times under threat but we didn't create enough chances.
"Considering our performance and the result of the game, I don't think we deserved anymore today.
"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.
"Our game lacked purpose, penetration and speed, all qualities we have usually but we didn't see that tonight.
"Maybe we thought we scored seven against Newcastle, we thought we would score again today.
"I felt that we lacked purpose in our game and it was more mental than physical.
"We prepared normally, we prepared well, and Southampton deserved some credit.
"They fought for every ball and were on their toes. They were fighting until the last second for every single ball.
"We did not have enough quality to take them out of position and take advantage of that."