The 22-year-old was excellent against Dinamo Zagreb on Thursday, grabbing himself a goal in the 2-0 victory.
Rice started playing for West Ham as a centre-half and has now developed into a quality midfielder, and Moyes thinks the England international can keep moving forward.
"He's played international football for his country but not for his club," Moyes said. "So I think it's something he's having to get used to as well. It's only the start.
"He's trying to take himself to the next level. He's a terrific player, he's getting better. He's shown it in his performance tonight.
"He was the captain of West Ham for the first time in Europe for a long time away from home, scores a goal as well which probably makes the game much more comfortable.
"So from that point of view, we have seen a real development. You mustn't forget he is still 22 years old, and a young boy with a big future and a big career ahead of him. One step at a time but he is doing really well for us.
"The thing about it [the goal] is his ability to surge away from people, the power and speed. It is a great trait he has got and we would like him to use it more.
"If you can remember the last game of the season last year against Southampton, it was a little bit similar to that goal when he broke away and scored.
"He had a bit of a ribbing because he does not score enough goals so he's beginning to stand up and we will have another very good goalscoring midfield player."
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