The Gunners gave a starting berth to the 18-year-old for their 3-0 group-stage win over Monaco.
Asked about Lewis-Skelly, Arteta beamed and stated: "Well, really proud moment. He's one of our own, 18 years old.
"He makes his starting debut in the Champions League and he's just a joy to watch him you know.
"It's a privilege to have the opportunity to give a chance to somebody, to start to change his career.
"He certainly took the chance and it's great that we can trust him, that he can play in this environment and on this level and I was really happy with his performance."
Whether the youngster can now earn more game time in the Premier League and Champions League, Arteta added: "He's good, he's been in contention. In pre-season, he opened our eyes to say I'm ready, the same as Ethan (Nwaneri).
"He feels comfortable in this environment, they can perform, they can compete which is important as well not just play and today he's shown that he's at that level."