Moyes revealed earlier this week that he told the striker a month ago he should follow the example of Wayne Rooney and increase his preparation workload - but Welbeck insists he has never slacked off.
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"Maybe, I haven't seen what he has said. Obviously, at Manchester United, I want to be working hard and I have been doing that ever since I was a young kid. I just want to keep on getting better and improving.
"Those extra hours on the training pitch, whether it be with the boys or individually, I am just looking to improve."
Welbeck also revealed that he is aiming to score more goals this season and does not mind which position he plays in up front, though he is keen to deputise for the injured Robin van Persie up front.
"I want some more goals, I can tell you that," he said. "I have got a figure in my mind, I want to score plenty more goals.
"Obviously it is not my decision about where my play. As I have said plenty of times before, I am happy to play for Manchester United in any of the attacking positions.
"Unfortunately, Robin [van Persie] has got injured. I might have a chance up front so I am looking to score some goals for Manchester United whilst playing as a centre-forward."