Two quick-fire goals after the interval, with in-form duo Olivier Giroud and Santi Cazorla once again on target, gave the visitors a lead to defend before Adam Lallana pulled Southampton level and Mathieu Flamini saw red late on.
The draw means both Manchester City and Chelsea can overtake the Premier League leaders if they win their respective fixtures but Wenger, whose side arrived late due to congestion around the stadium, refused to see their draw as a missed opportunity.
"I think in the first-half Southampton played very well and we didn't play well," he said.
"Southampton deserved the lead at half-time and in the second-half I felt we played well and it was a very good football game.
"We played in second gear and Southampton in fourth. They played at a higher pace than us, decided to stop us from playing and did it very well. It is difficult to maintain but they did it for 90 minutes and they did it very well in the first-half.
"You want the three points in every game but it is a difficult place Southampton. When you look at the overall record it can happen sometimes away from home you take only one point."
Flamini was dismissed with 10 minutes remaining for a two-footed challenge on Saints midfielder Morgan Schneiderlin but Wenger felt his player was unfortunate to be sent off.
"To me it looked harsh," he said.
"He got the ball. At some stage we have all the feet off the ground - when you want to run you need to put the feet off the ground.
"If you say that every time a guy makes the two-footed tackle it is a red card he deserved a red card. If you say was it a violent tackle I would say no as he played the ball. I don't know, the referee made the decision, we have to cope with it."
The France international will now miss the next four Arsenal fixtures, including Sunday's game against Crystal Palace, and Wenger's options in midfield will be further limited following a setback in Aaron Ramsey's return.
"Aaron Ramsey is out for longer than we expected as he had a little setback yesterday in training so I couldn't bring him here," Wenger confirmed.
"It is the same muscle. He felt it a bit again so we have to be cautious this time."
Southampton manager Mauricio Pochettino felt his side did enough to win the game and praised his players for not letting their heads drop following Arsenal's two goals at the start of the second half.
"I thought the team was outstanding," he said.
"We were sensational in the first half and did really well. It was total football. In the second half we didn't start so well and conceded two quick goals. I would highlight fact we were able to get back into it - we showed amazing character and we deserved to win in the end."
- Sports & Recreation
- Mathieu Flamini
- Olivier Giroud
- Adam Lallana