The visitors were hanging on at the end as Sunderland bombarded their goal.
Arteta said: "You have to win games like that. In the last five or 10 minutes they were hanging balls into the box.
"It's difficult to get the ball out when they do that, but we defended really well and Wojciech Szczesny made two or three outstanding saves. Criticism has to be constructive. We're not as high in the table as we have the ability to be, so we know we're there to be criticised. The only thing we can do is improve where we are in the league.
"Everyone knows we play really good football at times and create a lot of chances. Hopefully from now to the end of the season we will move upwards in the league.
"But we showed we can battle too. It's always difficult with 10 men."