Rice added West Ham’s second goal five minutes into the second half, as they began their Europa League campaign with an impressive 2-0 win in the Croatian capital in their first-ever European group game.
The 22-year-old picked up a loose pass on the halfway line, surged forward and fired between the goalkeeper’s legs to give the visitors a deserved cushion after Michail Antonio’s 22nd-minute goal.
Rice scored just twice for the Hammers last season, including a penalty, but found the net on England duty in Hungary earlier this month, and Moyes says he is working to go up a level.
“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.”
Rice celebrated his goal in front of the loudest section of home fans, aggravating Dinamo captain Arijan Ademi who raced over to confront the 22-year-old, causing a small ruck.
It was similar to Rice’s reaction for England in Hungary earlier this month, when he pretended to drink from one of the cups thrown at team-mate Raheem Sterling.
“That’s still the young player which we can see,” Moyes added.
The manager made five changes from the 0-0 draw with Southampton at the weekend and is likely to change his team again for the visit of Manchester United on Sunday.
Moyes believes the result underlined his squad’s strength in depth and says he is excited by West Ham’s potential.
“I’m really excited by the prospect of slightly not knowing how good they can be,” said the Scot. “I mean, tonight we brought in two or three different players, we changed it and we didn’t look any worse for it.
“The challenges will come. My target is to make sure that we’ve got European football after Christmastime and if you get to that point then you know that you start to involve other teams but one game is all it is and we’ve got to try and continue the level we’re at, and we’re at a good level the players are in a good place here.”
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