The Gunners won impressively 3-0, with Rice opening the scoring on Wednesday night.
Rice said at the final whistle: "A lot of teams now come here and play a back five, with four in midfield and one up front, so it's really hard to break down. To get that early goal really settled us and then it's just about being patient and not being sloppy. There were a few times we took too many touches and we nearly got caught out.
"In the second half it was really positive. We chose when to press well and in the end got two great goals, which was a real positive note.
"I was in the box and I just knew I had to get my knee over the ball. I set myself really nicely. A similar one got cleared off the line the other month against Ipswich, with the same technique, so to score tonight - and obviously it being my first Champions League goal - I'm so happy. Hopefully I can get many more in this competition because it's the best competition in the world."