"Aaron Ramsey is out for longer than we expected because he had a little setback in training yesterday (Monday). So I couldn't bring him here," Wenger said.
"It's the same muscle he did a bit again so we have to be cautious this time. Hopefully he's not out too long but he won't be available for Sunday's game (at home to Crystal Palace)."
Arsenal must also cope without French midfielder Mathieu Flamini, who faces a four-match suspension having already been banned this season, after being shown a red card by referee Lee Mason for a two-footed tackle on Morgan Schneiderlin.
"To me it looked harsh. He got the ball. At some stage you have all the feet off the ground, when you want to run you need to put your feet off the ground," said Wenger.
"If you say every time a guy who makes a two-footed tackle it is a red card, he deserves a red card. If you say, 'Was it a violent tackle?', I'd say no because he played the ball. But the referee made this decision and we have to cope with it."
Arsenal could have moved four points clear with a win at Southampton but were pegged back by Adam Lallana's second-half equaliser after Olivier Giroud and Santi Cazorla had given the visitors the lead following Jose Fonte's early strike.
The London side's slip up opens the way for Manchester City and Chelsea, two and three points behind in second and third place respectively, to take over at the top on Wednesday.
Free-scoring City visit fellow in-form side Tottenham Hotspur while Chelsea host struggling West Ham United.
"You want the three points in every game but it is a difficult place Southampton," said a philosophical Wenger. "When you look at our overall record it can happen that sometimes away from home you can take only one point.
"I think in the first half Southampton played very well and we didn't play well. Southampton deserved the lead at half-time. In the second half I felt we played well.
"We have shown a lot of character and resilience to respond to what happened to us in the first half (going behind).
"Overall I'd say it's a difficult point but a fair one. I wouldn't say it was a very, very bad performance, I think it was a very good football game and Southampton deserved some credit."