Mikel Merino struck early and Bukayo Saka scored in injury-time as the Gunners did enough to secure the win, with Arteta left pleased with those players who were rotated into the XI.
Arteta said afterwards: "I'm so happy. These are examples that the squad needs, the impact that they have in the team.
"Ben (White) hasn't played more minutes because Jurrien (Timber) has been excellent, and before that, because he was injured. But his attitude has been exceptional every single day. Then when you have to play and show your level, you do it because you are ready."
He also said: "It's incredible because we lost Big Gabi and Willy (Saliba), our two main centre-backs who played for a long, long time together. Then we had Mosquera and Piero (Hincapie) doing really well. Then we lost (Cristhian) Mosquera. We have to adapt again. But the fact that the boys want it so much I think is the reason why we continue to win games.
"We come off the back of a very, very demanding week emotionally, physically, at every level. Then we have to play three days later with one less day to recover than Brentford. I think we dominated the game.
"We created quite a lot of chances, big chances, but 1-0 against them. Understanding how dangerous they are every time they generate a set play or a throw-in is incredibly hard because it's always in the back of the mind that they don't need much to score a goal.
"But I think the part that I probably like the most is when the game was a bit open and they were getting some momentum. We took the ball, we pinned the ball down, we started to play. We have a lot of courage to get out of certain situations and score the second goal and win the game."