The Gunners survived a late scare to hold onto victory, brought about by goals from Eddie Nketiah and Bukayo Saka.
Arteta said after the game: "Very pleased. Always tough to come here and win, we've done it with a young team as well.
"I have a lot of faith in them. I think they are developing really well. They are willing and hungry and will only get better,
"We analyse opponents and try to generate situations that are favourable for our players.
"I was worried with their history in the last few weeks we would concede in the last few minutes.
"Our history with this cup is massive for the club. We need to take it step by step."