After putting seven past Newcastle in their last outing, the Gunners largely failed to test Saints goalkeeper Artur Boruc, with Guly do Prado's own goal providing their solitary breakthrough.
And the Frenchman bemoaned his side's lack of creativity after dominating their opponents in recent matches, but admitted a draw was a fair result with the hosts defending resolutely.
"Considering our performance I don't think we deserved more today," he told reporters. "It's two points lost if you look at the target we had over Christmas.
"We were not very good. Offensively we didn’t create enough. I felt we lacked sharpness and desire really to get in the box and create what we can do.
"It's frustrating and disappointing because we didn't create a lot today after having scored five at Reading and seven against Newcastle.
"Our game lacked purpose, lacked penetration and lacked speed, all qualities we usually have.
|40/1||Theo Walcott is 40/1 with bet365 to finish as the Premier League's top goalscorer this season
"Maybe Southampton deserve some credit as well. They did fight for every single ball they were on their toes. Did we underestimate Southampton? I hope not."
After scoring a superb hat-trick against the Magpies last time out, Theo Walcott struggled to make a similar impact upon returning to his former club.
The 63-year-old refused to blame the England international, though, instead suggesting that he did not receive good service.
"I believe overall collectively we were not good enough," he continued. "I wouldn’t like to go into individual performances and judgements but [Walcott] didn’t get a lot of service today [and] it wasn’t easy to play up front."
The Gunners boss also once more ruled out the possibility of Thierry Henry returning to the Emirates Stadium on loan again, but did state he would be "active" in the January transfer window.
Unlike Wenger, Saints boss Nigel Adkins was buoyed by his side's performance, insisting it was indicative of the south coast club's recent improvement.
"You look at the goal we've conceded and it's that little deflection," he added. "I thought we had a good defensive shape about ourselves. I felt tactically we were bang on in restricting Arsenal to two very limited opportunities.
"It's only two defeats we've had in ten games. You look at how far we've come [since the 6-1 defeat to Arsenal earlier in the season]."