Southampton captain Jose Fonte has said that the team must learn from their mistakes if they are to convert their dominance into results.
Fonte's underhit back-pass was intercepted by Van Persie, before the Dutchman slotted the ball past Fraser Forster for the opening goal.
"It was frustrating," Fonte told Southampton's official website.
"I thought that, apart from my mistake and that free kick in the second half, we weren't in danger. They didn't create much, whereas we were in control of the game.
"We were dominating, but we have to stop these mistakes and to try to avoid them because they're costing us. When you play in a game like this and play in the way we did – especially in the first half – then I think it's disappointing for everyone."