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.
And 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.
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"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 practising his finishing every day. Whether it be taking free kicks, shooting from tight angles, bending them in, whatever it may be, Wayne is practising and I told Danny that he needs to be out there practising 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 practise into operation.
"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.
"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."