England forward Welbeck scored just once last season after having his appearances restricted by the arrival of Robin van Persie.
He made a flying start to the current campaign by scoring twice in the opening game at Swansea but then experienced a goal drought for his club before netting twice again in Sunday's 3-0 win at Aston Villa.
Moyes said: "We had a word with him about a month ago and said he needs to be the last off the training field.
"Wayne Rooney is out there practicing his free-kicks, his finishing and shooting from tight angles every day.
"Danny needs to be out there, even if it's 15 minutes at the end.
"The young boys here are educated to keep improving and practicing. Sometimes, without knowing, you can slip away from it."
Welbeck's contribution at Villa Park was perfectly timed with Van Persie sidelined for four weeks due to a thigh injury.
Moyes added: "He stood up without Robin, took it on and scored two.
"We challenged him on Sunday and said he needs to stand up. He took the bait. I think he said 'okay, I'll show you'."