Gabriel Magalhaes and Jurrien Timber scored in the second-half for the Gunners.
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Arteta later said: "Very happy, it was a special night in this incredible stadium.
"I think we deserved to win the game. We changed the team due to a few injuries, but what an energy in the stadium.
"We got into the second half and we changed a few things - the team was superb.
"The team needs every possible result to win the game - let's continue that."
On Liverpool dropping points at Newcastle, he added: "I didn't know as I was so happy celebrating in the dressing room.
"We got that news, but it is difficult to win this league. It is still very early."