The Gunners lost for only the second time in the top flight this season as James Tarkowski's header on the hour mark gave Sean Dyche victory in his first game as Everton manager.
Arsenal have now lost on each of their last three visits to Goodison Park.
With champions Manchester City not in action until Sunday against Tottenham Hotspurs, Arsenal's lead at the top of the table could be down to two points should victory go the way of Pep Guardiola's side.
But after a bad day in the office, Arteta is bent on rousing his charges once again, with their next games coming against Brentford and Manchester City.
“We had loads of the ball and we generated many chances, but we lacked that purpose and quality in the final third," he told BT Sport.
"Then we conceded and they slowed the game down and we struggled.
"They do this to every team. Their physicality is their strength. If you want to control the game against them you have to control this. We did not do that.
"We needed more composure and to better control the game emotionally. We gave away so many unnecessary free-kicks and that's what they want.
"Today I love them much better than the week before or a month ago. It is easy to be next to someone when they are winning well. I am still so proud of all of these players, they deserve it.
"This is not going to be a rosy pathway. This is going to be tricky and we will have to dig in and play much better than we did today."
