Beckford scored his first two goals for the Toffees in their 3-0 pre-season victory over Moyes' former club.
He hobbled off towards the end of the match after picking up a knock but Moyes does not believe it is a serious problem.
"I don't think it was bad. He got a kick on the top of the foot when he went to strike it and had to come off," Moyes told Sky Sports News.
"Nothing to worry about. I think he will probably be back training on Monday or Tuesday."
Louis Saha netted Everton's other goal and Moyes is excited about what the Frenchman can bring to the team if he steers clear of injuries.
The Toffees manager stated: "Louis played well and he's looked quite sharp.
"I think everyone knows if you can get a fit Louis Saha then you have always got a chance of getting a real good player and plenty of goals hopefully."