Bukayo Saka and Gabriel Martinelli struck the goals for the hosts.
Afterwards, Arteta said: "I am happy with the points after losing [to Liverpool last weekend]. You have to win straightaway. Overall I'm pleased.
"The word was we had to be patient. We had to play with urgency and rhythm. That's what we did in the second half. We found spaces and that's how we scored the goals.
"When you have chances you have to put them in the net. In the first half we shot from every range without composure."
On Bukayo Saka's injury, he added: "He wasn't comfortable. He felt something."
On the second goal struck by Martinelli, Arteta enthused: "The movement, the pass from Tomi is great. It's really difficult to keep the ball down when it's flying over your head but that's what he can do."
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