With Manchester United having to work without Wayne Rooney and Robin van Persie at times, the manager wants the young forward to push on after his encouraging recent form.
The England international only found the net twice last season but has already claimed seven in all competitions during 2013-14 - making him the club's third-highest scorer, behind Wayne Rooney and Robin van Persie.
The 23-year-old came off the bench to score the winner against Norwich City on Saturday and Moyes has been impressed with the young forward but wants to see more from him in the second half of the season.
"We have said to him we are trying to keep his finishing up," the Scot told reporters. "I think he can keep his efforts up, his levels up, even better. He got one [league] goal last year and now he is on seven for this season. It could be better but you have got to say it is going in the right direction.
"With the second half of the season to go, he should be certainly looking to score 20 goals. We need him to do that because, when you don't have Wayne and you don't have Robin, then you need people to step up to the mark. In quite a few of the games recently he has done that for us."