Arsenal reach the final eight 9-3 on aggregate, where they will face Real Madrid.
Sterling laid on both assists for Arsenal on the night and Arteta said: "I was very happy for him, and for a lot of individuals as well that haven't had a lot of minutes recently.
"We could tell in the second half, that we lacked the physical capabilities to make certain efforts and runs and certain arrivals into certain spaces in the right time. But overall, very happy that they got the minutes and they responded."
On Sterling's influence on Arsenal's two goals, Arteta said: "Yeah, in the second one, and then he does the last final action as well that he can score. The keeper makes a save and the way he tracked back as well after the corner in the last action when he got booked, that's the kind of player that we want to see."
Asked whether Lewis-Skelly is a long-term left-back or midfielder for Arsenal, Arteta continued: He can play in both positions and in relation to the player that he plays as a full-back as well, they can interact and if they change positions.
"He played as a six. He was developing in the academy as a six as well, so what he's doing this season is something new for him. So I think it's much more to it to play in midfield. He's done really well tonight as well. I think he was very, very consistent in his actions and I'm really happy with what he's doing."
On how they'll tackle Real Madrid, Arteta also said: "Last year we played Bayern, and with the history of those clubs and how consistently in the last 20-25 years being there, and we were riding there in the home game, we had them on the ropes.
"They escaped and when we were there we were a bit short to get to that final stage. So hopefully we will learn we are better than then and we can make it happen."