Moyes was delighted with his team's performance, and particularly the efforts of England full-back Baines.
He said: "Ashley Cole is the best left-back in England and I have always thought Leighton Baines is behind him.
"But I said last week before we played Chelsea, I think the gap between the two of them is getting much closer.
"He is disappointed he has not scored three goals tonight, Bainesy."
Baines was delighted with his side's victory, describing the result as "massive".
"It was a massive three points," Baines told Sky Sports 1. "We were off the back of a defeat and Newcastle are fighting at the moment so we knew it would be tough.
"They set off at a hard pace but we fought back."