Twice Everton jumped ahead after Newcastle equalised, including on 83 minutes as Thierno Barry struck the winner.
Moyes said afterwards, "I expect it… Away from home, we've tended to find a winning solution, or maybe not a solution, but we've been able to get better results away than we have at home.
“I think the players did a great job today, I was really pleased. Beto gets his goal and did a good job all round.”
Fellow goalscorer Beto started ahead of Barry and Moyes also said: d: “You have to do well.
"We accept that you don't always score goals, but you need to do really well for the team, and hold the play, hold the ball up, and join in, and be creative. So we just saw that there's been a couple of games Barry's been a little bit off it, so we went with Beto.”
Moyes also handed Dwight McNeil a first appearance - as a starter - since his move to Crystal Palace.
The Scot added, “Well, the club pays his wages, so I don't think we should really need to support him too much. I don't treat him any differently than I would treat any other player.
“I just told him to get on with it and he has done so. He's trained really well this week and deserved the opportunity to start the team.”