The Gunners won 3-1, with goals from Kai Havertz, Gabriel Martinelli and Bukayo Saka after Cameron Archer had given Saints the lead.
Martin said afterwards: "I think the game panned out how we though it might. They had the ball but I loved the way we defended. We asked for more courage on the ball and I thought we showed that. We had some really brilliant moments in the second half. When we scored we'd limited them to few chances.
"But they scored too quickly after that, it's a mistake and we get caught losing the ball.
"I feel so much more positive and proud of my team than I did on Monday night, and we played against one of the best teams in the country. If we play like that in the next block of games I'd be very happy.
"Our mentality at 1-1 was much worse than when we scored. Emotions, it's nice to score a goal, it's a nice goal, but we have a problem and we concede.
"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 today. I loved all of that and if we continue to grow I'm going to be happy. "