The Scot was pleased to see his striker net twice in Sunday's 3-0 victory over Aston Villa but insists he must continue to show a greater desire to improve in training.
Welbeck netted twice against Aston Villa on Sunday in the absence of the injured Robin van Persie to take his season's tally to five, having scored just two goals last term.
While Moyes is pleased to see signs of progress, he is adamant his striker needs to show the same desire to improve his finishing as Wayne Rooney.
"Danny needs to score more goals," Moyes told reporters. "We had a word with him about a month ago and we said that he needs to be the last off the training field. Wayne Rooney is out there practicing his finishing every day. Whether it be taking free kicks, shooting from tight angles, bending them in, whatever it may be, Wayne is practicing and I told Danny that he needs to be out there practicing every day even if it is just 15 minutes every day.
"He did take heed. He is out there now. If you remember the goal he got at Villa on the right and the chance he just pulled past the post, I thought, well here you go put your practice into operation."
Moyes went on to say that Welbeck, even from a wide position, can give the team added attacking options, but only when he is able to get goals.
"Danny plays off the left for England as a wide striker and when he plays those roles he is great at getting in the box and it gives you a feeling of having an extra forward. He is a really good worker for the team," he said. "But I think if you asked Danny he would say he is a striker. What gets you a game as a striker? Goals. Whether you score them from inside the box or outside the box, from distance or tap-ins, if you want to be a striker in the Premier League and especially at a club like United you have to be a goalscorer.
"Is he a goalscorer? What I will say is that everybody told me he had only scored two last season but this year he has scored five. So that is a positive start for him. All round Danny has a lot of attributes and he just needs to say I am going to have to take this onto another level. We are trying to get him to do that."