Welbeck scored just once last season after having his appearances restricted by the arrival of Robin van Persie.
The 23-year-old doubled that tally in the first game of the new campaign at Swansea before experiencing another lengthy drought, leading to some United fans to raise criticisms about his contribution.
Moyes is certainly looking for more from Welbeck, and the Scot revealed it was his promptings that got his forward doing additional sessions.
"We had a word with him about a month ago and said he needs to be the last off the training field," said Moyes.
"Wayne Rooney is out there practising 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 practising. Sometimes, without knowing, you can slip away from it."
The extra work appeared to pay off on Sunday when Welbeck scored twice in the 3-0 win at Aston Villa.
It was a perfectly timed contribution given Van Persie is facing four weeks on the sidelines with a thigh injury.
"He stood up without Robin, took it on and scored two," said Moyes.
"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'."
Source: PA
Source: PA