Rice scored twice as Arsenal won 3-2 at Dean Court.
Arteta said afterwards: "I really love today the next step of the team in terms of individual personality and presence. I think what Gabriel Magalhaes has done after making a big mistake to concede the goal, the way he reacted to that, the way he played afterward, the way he transmitted energy after that, it was remarkable.
"And Declan, another one. Every hour for him was important to be able to be available today. We didn't know for how long. So in the manner that he competed, played and on top of that scored two goals, I think it was outstanding. And a really big message for the team.
"To chip in you have to do a lot of things. First of all you have to get into those positions. He has the ability when he gets into those positions to put the ball in the back of the net. He's done it in a very similar way in both actions. And he's very consistent there."
On whether Rice is now one of the best midfielders in the world, Arteta continued: "Yes, for me yes. For me the ones that we have are the best. Declan is constantly adding things to his game. He's constantly adding things to his role in the team. I don't see where he can stop because he can still improve in a lot of areas and he wants to improve. He's such a pivotal player for us.
"Because he was so disappointed not to play against Villa, he really wanted it. He tried in the morning, it was nowhere near a possibility. He wanted to train the next day, it wasn't a possibility. Until the last minute I asked him, how are you feeling? He said, I'm in. And he showed that he was big time in."
Arteta also revealed: "I think we sit down together and set goals. Setting goals is not enough. You need a plan to implement and make it happen. He's extremely consistent in everything that you ask him to do and everything that he really wants to do. That's what makes the difference. First of all, he has the ability and the qualities to achieve that for sure. But then you need the consistency to do it. He's doing it every single day and then you see that kind of performance."