The Black Cats were competitive in the first half at the Stadium of Light before dropping their standards completely in the second lot of 45 minutes, allowing Romelu Lukaku to score a quick-fire hat-trick.
After the match, former Toffees boss Moyes spoke of his side's display, indicating that he was in disbelief that a player of Lukaku's quality was twice left alone in the box to head home delivery from the outside.
"We were really poor in the second-half," Moyes told Sky Sports.
"Defensively in the second-half we weren't in the right positions to defend crosses.
"Two of their goals came from crosses. I couldn't believe we had no defenders in the middle of the goal to defend it, especially against Lukaku.
"It's something we'll need to look at but we are putting together a new team so it's going to take time.
"There were some good moments but I was really disappointed, especially with the last 30 minutes or so."
"We just didn't do the basics in defence correctly and because of that we got punished."