An early goal from Mikel Merino was enough for the Gunners on the day.
Arteta admitted afterwards: "We should have done much more but we are very happy and it was an important game. We play a top opponent and the team played with an unbelievable spirit and now we go to the international break.
"The only thing we can do is try to win our matches. If we do, we are in a better position."
On Merino playing up front, Arteta continued: "We have had top players out for many many months. Our team has an incredible resilience. Mikel really wants to do well, he has never played that position before but he is scoring goals.
"He is a really dangerous player in the box and he can help us. Really pleased, even physically it is a very different game to play as a nine."
He added, "We did enough to deserve to win the game. Now we have the international break so let's take a chance to breathe and bring some players back hopefully.
"We weren't able to finish some of the actions. I really liked the attitude of the team.
"It was a big game and we wanted to win against a top team."