Rice struck both goals from free-kicks - a first for his career - as the Gunners won the first-leg of their Champions League quarterfinal 3-0.
Afterwards, Rice beamed: “I’m speechless, this has never happened to me before!
“This is the quarter-final and we know how much this night meant. It's a real historic night for the club. I'm so happy.
“They (his free-kicks) were really good. To be honest with you, I'm not used to all of this praise and media and just people saying how good the free-kicks were! I've seen them back a few times now but I think I'll be up watching it all night. It's an incredible moment, I can't believe it.
"As soon as I hit the first one and it went in, I thought 'that's my first ever free kick!' And then I just had the confidence over the second one. I just thought, 'why not? What have I got to lose?' I was going to go over the wall and I thought: 'I've got the keeper's side, on a good one.' I've been practising that a lot.
"So, yeah, two went in and they're just magic moments. They're going to stay with me forever."
Rice was also eager to hail the home support for the result.
“Credit to the fans, they were unbelievable tonight," he added. "From the moment we turned up in the stadium to the kick off and to the 90th minute, they were outstanding and we're going to need everyone at the Bernabeu next week because it's going to be a massive night for us.
“This is probably up there with the best moment in my career in terms of the goals I've scored. I think the free kick is probably the best goal I've scored. I think winning next week would probably top that, by going into the semi-final and producing something special for this club.”