Beto's double and Iliman Ndiaye's goal saw Everton sweep aside Chelsea 3-0 at Hill Dickinson stadium.
Moyes said of Beto: “I think his all-round game tonight was much better. His link-up play was better. And he gets two goals tonight in a big game. It says a lot. I keep saying that.
“I've said it in every interview… He's a great boy to work with. He's incredibly humble. He tries to improve himself every day.
“And sometimes when you work like that, you get good fortune and good luck. I'm not saying it was good luck, but we certainly got what he deserved from the work he puts in.”
Moyes also declared James Garner was “head and shoulders” the best player on the pitch and praised goalkeeper Jordan Pickford for two “wonderful” saves from Enzo Fernandez.
He added: “He probably just missed out on something (at Arsenal) last week a little bit. Today, he made up for it, definitely. He's an excellent goalkeeper.”