Arsenal needed a controversial late penalty to see off the Saints and secure back-to-back Premier League wins.
"If you don't concentrate for 90 minutes, you lose points," he said.
"So we concentrated and we were in the game until the end, and that's what gave us the win."
Mustafi was also delighted to make a successful debut for Arsenal and thanked the fans for their warm welcome.
He added: "I'm happy for the three points, first of all.
"But I'm also happy with how the supporters have received me here and how the team have made me feel part of it."