Goals from Jordy Clasie and Ryan Bertrand secured a 2-0 win for the Saints and a first League Cup semi-final in 30 years at Emirates Stadium on Thursday (AEDT).
Wenger made 10 changes from the weekend's 3-1 win over Bournemouth and was rewarded with the Gunners' first defeat since the opening day of the Premier League season.
"It was one of those nights where it looked like we can play for two hours and not score a goal," the Frenchman said.
"We didn't have enough urgency in the first half. We were weak in some departments and we paid for that.
"I have no regrets over selection, I regret we lost the game."
Wenger's opposite number Claude Puel was delighted with a strong display from his side, who looked far more cohesive, despite making eight changes.
"I enjoy this win for all of the squad and for the fans, because it's a good answer to keep all of our possibilities in every competition," Puel said.
"It was an objective of the team to qualify for the semi-finals after the winter.
"It was a strong game, with good solidarity. We moved the team at the start with different players and the answer from them was fantastic.
"We played a very good game and to qualify for the next round is very important. We now get to play in a semi-final and that's great for the players."
Southampton will play Liverpool in the semi-finals, having lost 6-1 to the Reds in the same competition last season.