The Cameroon international was left out of the opening Premier League fixture against Sunderland as he finalised a ?15m move to Barcelona.
That meant Arteta was asked to operate in a deeper midfield role and despite having to settle for a 0-0 draw against the Black Cats, the Spaniard was encouraged by his new partnership with compatriot Santi Cazorla.
"I felt really comfortable when I played with Alex last year, he was a terrific player," Arteta told the official Arsenal website.
"But if he and the club decided that the best option was for him to leave we have to accept it. I think we are good enough to carry on without him.
"I think we are looking good. We looked really organised on Saturday, just maybe in the final third we didn't take the chances we should have done.
"It will take a while because there have been some new players coming in and we are building a new team.
"We have lost some important players but we know that our new players can make the difference as well. We will have to give them a chance to settle into a new place."
