The Gunners missed out on a spot in the semi-finals after losing 2-0 to the Saints.
After the game, Wenger told reporters: "I'm disappointed. We had a disappointing performance, particularly in the first half. 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."
Arsenal's opponents will take on Liverpool in the semi-finals, while Manchester United will face Hull City.