The England forward came off the bench at Norwich to net his fourth goal in five appearances as United recorded a fourth straight Barclays Premier League win to move within striking distance of the top four once again.
Wayne Rooney missed the trip to Norfolk as he rested a groin problem, but should return for the New Year's Day clash against Tottenham, while Robin van Persie is also set to step up his recovery from a thigh injury which has sidelined the Dutchman since mid-December.
Moyes sees no reason why Welbeck - who now has seven goals for United to add to his three for England - cannot push on to make his mark on the run-in.
"We have said to him we are trying to keep his finishing up. I think he can keep his efforts up, his levels up even better," said Moyes.
"I think Danny has responded, he is saying 'hey this is quite good I am beginning to score some goals and getting recognised for that as well'.
"He got one goal last year and now he is on seven for this season.
"It could be better, but you have got to say it is going in the right direction.
"With the second half of the season to go, he should be certainly looking to score 20 goals.
"We need him to do that because when you don't have Wayne and you don't have Robin, then you need people to step up to the mark.
"In quite a few of the games recently he has done that for us."
Javier Hernandez was started at the head of the United attack on Saturday, and Moyes feels his side need to have plenty of options.
"I don't think at Manchester United you have only two players to do the jobs. You have got to have more, like in these games you would never be able to cope when you pick up injuries," said Moyes.
"I see it more as a squad rather than any one. Chichirato is part of that, who is a great goalscorer too."
Despite United's upturn in fortunes which has seen them into the semi-finals of the Capital One Cup and the last 16 of the Champions League, Moyes is determined to keep everyone grounded.
"That is my style," the Scot said. "We are just trying to move along and we have nothing to shout about here at the moment."