Saints had the lead through Cameron Archer before the Gunners fought back through Kai Havertz, Gabriel Martinelli and Bukayo Saka.
Arteta said afterwards: "The start was exceptional, the dominance, the chances. It was unbelievable not to go one, two, three goals up.
"We conceded the goal and then it was game on. I thought the team reacted with a lot of authority and I am happy the team can react like this - but not happy after the chances we had that we had to go through that.
"The substitutes changed the energy and also the feel in the crowd. We won in the end and I think we deserved it.
"The way we started was phenomenal but we didn't get our reward. We had a difficult context at 1-0 but we did it."
On Havertz, he added: "He's really hungry, such an intelligent player, he is so focused to achieve what he wants and was exceptional again.
"We lost so many players last international break, very difficult schedule but this team finds a way. A good platform to continue the season."