The Gunners won 1-0 at Hill Dickinson stadium thanks to a first-half penalty converted by Viktor Gyokeres.
Arteta remarked afterwards: "Very happy. We put in a very solid performance. It's a very difficult place to come against a team that are very organised.
"They can create very chaotic moments in the way that they play, but I think we controlled it really well, scored the goal and in the second half we talked about scoring the second one.
"So, we went for it, had about three or four big chances, hit the post twice and probably the margin should have been bigger. But yes, defensively, again another clean sheet. We haven't conceded any chances throughout the game, so a positive evening."
On Gyokeres getting back on the scoresheet, Arteta was pleased.
"(I am) very happy. It's a really important goal to win the game," he added. "I love that the players took ownership to decide who the taker was going to be, and it worked - so a good decision overall."
The former Everton captain also reflected on the Toffees' new stadium.
"Yes, it's unbelievable. If I had to pick a place, probably it would be this one. I take the opportunity as well to congratulate everybody at Everton and all the people who have worked to build this incredible stadium.
"I was shocked - I didn't expect such a beautiful place and the atmosphere that they created, so well done to all of them."