A 0-0 draw at home to Sporting CP on Wednesday saw Arsenal win their quarterfinal tie 1-0 on aggregate.
Rice wore the captain's armband in the absence of the injured Martin Odegaard and Arteta explained afterwards: "They made a decision because Declan has earned it as well.
"The status, the role, the way he's taking ownership as well in difficult moments. He's a great leader, he's a top player for us, and I love the players to take ownership."
Arteta also said of facing Atletico Madrid in the semifinal: "I watched them yesterday. That stadium is special. Those are the moments we want to live together as a team right now, so enjoy tonight.
"Tomorrow we will start to prepare for the weekend and then we will think about that."
