The Gunners avenged their FA Cup defeat to Saints with a 3-1 victory at St. Mary's.
But Arteta quickly turned his team's attention to their next game where they'll welcome Manchester United to the Emirates.
"We were really good right from the start," Arteta said. "We conceded and reacted straight away. On the ball we improved a lot.
"We got out of trouble and created chances. Our pressing was excellent. We managed the game when we went to 3-1 and were good on the break. It was a strong performance. Pepe was really good, he deserved his chance and took it.
"Saka has been very consistent, we have played him in different positions but he has adapted really well. It was a really strong performance from him again today.
"Southampton are a really good side, and the way we understood what the game required in each moment showed a lot of intelligence.
"We still have a lot to do. Be humble, train good and prepare for the next game."