He accepted responsibility for Arsenal's meek FA Cup exit at St Mary's, with the Premier League leaders missing a chance to reach Wembley.
Two weeks after a Carabao Cup final defeat to Man City, the injury-hit Gunners lost to Championship opposition in a lively atmosphere.
Ross Stewart put Saints ahead, and Leo Scienza then struck the crossbar before substitute Viktor Gyokeres equalised for Arsenal in the second-half.
But Saints secured their place at Wembley as Shea Charles came off the bench to clinch a memorable 2-1 win, which Arteta accepted as fair.
He said: "I am very disappointed in the manner in which we lost the opportunity to go back to Wembley. We had many periods of dominance.
Well that was a very fun evening. 👊#SaintsFC pic.twitter.com/lgmukwQmVK
— Alfie House (@AlfieHouseEcho) April 4, 2026
"We didn't capitalise on our chances enough. When you defend the box in the manner we did, you're going to put yourself in a really difficult position.
"They did capitalise on that, and that's the reason why we're out. I want to congratulate Southampton, I think they are a really good side.
"It's not a coincidence they are on the run they are. They were far more efficient than we were when it mattered. That's why they are at Wembley.
"I wish them all the best. We've played against every kind of behaviour from the opponent. We've played 51 games and won in different ways.
"I think it wasn't about that [tactics]. Without taking any credit from Southampton, it was related to something that we have to do a lot better."
Saints will head to Wembley for the FA Cup semi-final over the weekend of Saturday, April 25 and Sunday, April 26. The date will be confirmed soon.