Beckford struck twice in the first half to ease the Toffees into mid-table in the Barclays Premier League with a 2-0 success at Goodison Park. Beckford, 27, has had a difficult first season in the top flight after moving from Leeds last summer but now has eight goals for the campaign and appears to be finding his feet.
Moyes said: "When we brought him to the club the idea was we brought him on slowly and we had to put him in a bit too early. But I always thought if he got his chance and played some games he would get goals and he is proving that."
He added: "If you move up the divisions you have to try to compete with better players. The defenders are better, they are stronger, faster and have better concentration. You have to move up and learn that.
"It has been a big step up for him - it is for any player to jump up two divisions - and it was going to take time.
"He has got to improve on other aspects of his game but I think his movement in the box is as good as I have seen from a lot of the best. He can lose defenders and go one way and then the other. He is fantastic at that."
Everton's win was only their second in six league outings but built on last week's memorable FA Cup fourth-round replay success at Chelsea.
Sunderland were competitive throughout the first half and almost cancelled out Beckford's opener when Tim Howard tipped a thunderous Stephane Sessegnon drive onto the bar. But the second goal blunted the visitors' attack and the Black Cats surrendered to a fourth successive defeat that could have been more emphatic.
Moyes said: "I thought we did a good job, we were in control for most periods. I'm maybe a little disappointed we didn't add to our tally.
"I thought we might have scored more goals but overall we won 2-0 and I've not been able to say that too often in the Premier League this season. Thankfully we got those important points."
Source: PA
Source: PA