The Gunners were met by boos from frustrated fans as they saw their side unable to beat Saints goalkeeper Fraser Forster, despite 11 shots on target.
Wenger said: "We produced quite a good performance, especially in the second half when we created 10 goal chances.
"At the end of the day we came out with no goals.
"I believe the performance we wanted to produce was there, but we cannot be happy with the way we finished our chances.
"I think what's most disappointing is some players missed some chances that usually they would take.
"Our finishing is very bad at the moment - we have played three (league) games now without scoring a goal
In all those three games we had chances that we didn't take
At that level it's important."
Arsenal were the only team in the top six of the Premier League who failed to win on Tuesday night, and Wenger was frustrated at the result because he knew his side could do better
He said: "We started slowly but in the first half, a bit nervous because we lost our last game at home but in the second half it was one-way traffic.
"We still couldn't score
We didn't make enough of our set pieces, we didn't take them well, we didn't finish well
"It's just that our finishing was very poor.
"It's maximum frustrating, when your team puts the energy in and creates the chances.
"When you have no chances you come out of the game thinking 'Okay, there was not more in it.' When you come out and you think there was much more in the game like that (tonight), when you have our ambition of course it's frustrating."
Southampton manager Ronald Koeman was delighted to keep a clean sheet at the Emirates Stadium but he believes his players were not at their best in the match despite Forster's impressive performance.
He said: "Normally we are defending better than we were but the season is difficult, we have got the confidence back.
"It is now our fourth clean sheet in a row and that is giving confidence to the players.
"In the last few weeks our opponents have played with two up front and I prefer to play with three at the back but Arsenal play with three up front and if you put five defenders you miss one or two players to control the midfield."
Source : PA