The Gunners bounced back from Cameron Archer's opener to earn their 400th Premier League home win on Saturday, with Kai Havertz, Gabriel Martinelli and Bukayo Saka on target.
Arsenal enter the international break in third, hot on the heels of leaders Liverpool and level on points with Manchester City.
They also continued their impressive record against Southampton, extending their unbeaten run against them in the top flight to 25 matches (W17 D8), but the hosts were made to work for the win.
Arteta's side registered 14 shots in the first half with an expected goals (xG) total of 1.15, though their only shot on target came in stoppage time courtesy of Thomas Partey.
The introduction of Martinelli, Leandro Trossard and Mikel Merino prompted an improvement in attack shortly after Havertz's leveller.
"The start was exceptional, the dominance, the chances. It was unbelievable not to go one, two, three goals up," Arteta said.
"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. This team always finds a way.
"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."
Arteta also lauded Saka's performance after the England international took his goal involvement tally to nine for the season with his strike coming after two assists.
This campaign, only Erling Haaland and Cole Palmer (10 each) have been involved in more goals than Saka.
The 23-year-old has also taken on the role of captain in Martin Odegaard's absence, something Arteta believes Saka is embracing.
"For sure. That's the maturity and steps players have to do. He's been in the team long enough to earn the right to have that role. He believes in that," Arteta said.
"He has the capacity to change and decide games like many other players. If we want to be at the top, sometimes players have to create those moments, and he's certainly done that again today."
Southampton, meanwhile, are now without a win in their last 20 Premier League matches, equalling their longest top-flight winless run (a run of 20 between August and December in 1969).
But they had their moments to level the contest, with Tyler Dibling's deflected effort and Taylor Harwood-Bellis' header striking the woodwork prior to Saka's settler.
"I feel so much more positive and proud of my team than I did on Monday [after a 3-0 defeat at Bournemouth], and we played against one of the best teams in the country," Russell Martin told BBC Sport.
"If we play like that in the next block of games, I'd be very happy. I think we're learning and growing, and we're on a journey. But we're doing it under huge scrutiny and the intensity of the Premier League.
"I have to keep the guys on track and on path. There's a lot to be frustrated about, we don't have enough points on the board and a win yet, but I loved all of our resilience."