The home side took the lead at the Emirates Stadium through Pierre-Emerick Aubameyang, but second-half goals from Jorginho and Tammy Abraham turned the game on its head.
But Luiz has praised his “intelligent” manager and tipped Arteta to reach the very top.
“For me, Arteta is going to be one of the best coaches in the world,” the Brazilian told Sky Sports. “I have had the opportunity to have many coaches during my career.
“He is intelligent, he was a player, he is clever. I think he’s going to be one of the best, but it’s part of our job to help him do that, especially in the beginning because everybody doubts.
“But I really trust in this philosophy, I really trust in the way he sees football. That’s why we could see Arsenal dominate the first half with amazing football, with a lot of quality. I think if we scored the second goal, it would have been a different game.
“He knows football. When you know football, it is much easier to explain. It’s much easier to try to help and it’s much easier to understand the heads of the players on the pitch. It’s not an easy job for him, especially coming in the middle of the season.
“He didn’t choose the players or anything, but he’s going to try to do his best and we as players have to try to do our best too because this club deserves to shine. It deserves to play amazing football like in the first half.
“We are not in the best position in the table. It has not been a very good year for us. But there is still the possibility to improve, to learn, and to do what we did in the first half.
“I think everybody saw a team with personality, with ideas, with a connection with the fans, with top players.I think Mikel is trying to impose his philosophy as soon as possible.
“We have a lot of players with talent and a lot of players who are going to be top players in the future. They are trying to learn quickly. Then it is up to us to try to get some points and results because we need that.”