Wenger had been hoping to win the competition for the first time, but instead his decision to make 10 changes backfired with Southampton winning 2-0 to end his side's 19-game unbeaten run.
Midfielder Mohamed Elneny was the only survivor from Sunday's Premier League win over Bournemouth, but even Granit Xhaka and Alex Oxlade-Chamberlain coming off the bench failed to make an impact.
"I regret that we lost the game. We had played well until now," said Wenger.
"If you look at the players who played well tonight (Wednesday), some of those who did not play tonight were on the edge.
"In midfield we had (Francis) Coquelin, (Aaron) Ramsey, Elneny, Xhaka, (Lucas) Perez... (Olivier) Giroud was injured. We had (Alex) Iwobi, one of the regular players in the first team.
"The problem wasn't there. We had players who are used to top-level competition. But we didn't have the right urgency.
He added: "I'm disappointed. We had a disappointing performance, particularly in the first half.
"I think we were not good enough defensively and gave cheap goals away in the first half.
"It was better in the second, but it was one of those nights where you look like you could play two hours without scoring a goal.
"We didn't have enough urgency in the first half and were weak in some departments. We paid for that. We were not incisive enough in the first half especially.
"They played deeper in the second half and were sharper than us and fitter. If you give someone a handicap of two goals, against a Premier League side it's difficult."
Southampton are through to their first League Cup semi-final since 1987, when they were beaten over two legs by Liverpool, the same team they face in this year's semi-finals.
Manager Claude Puel was happy with how his team performed. "It was a great performance because this game was a different profile," he said.
"We were clinical in the first half, with two goals from two chances. I like this.
"After, in the second half, we had many chances to score another goal and make the game safe against a good team.
"It was a fantastic game to achieve that result: good solidarity, good attitude. I enjoyed what my players did.
"We have a chance to play a semi-final, home and away, in the second half of the season. That was the objective.
"(There are some) very important games in the future."