The Toffees picked up a fine win at the Liberty Stadium after a dominant performance but the 49-year-old also took time to praise Tim Howard who kept the home side at bay
Goals from Victor Anichebe, Kevin Mirallas and Marouane Fellaini sealed the victory, with the Toffees enjoying several more chances to have won by a greater margin.
Despite their constant pressure on the home side, Swansea had chances to score themselves and Moyes hailed his goalkeeper Tim Howard after several smart saves secured a clean sheet.
He told Sky Sports: "The result's always the most important thing but the performance matched the result as well.
"We could have scored probably six or seven goals, but they had three or four good opportunities which our goalkeeper thankfully made a couple of really good saves as well.
"That was important but I thought you'd be talking about the amount of chances we made and the opportunities we had in a game that we won 3-0.
"A lot of the games are like that at the moment. A lot of the Premier League games are lots of open action, and that's why they get chances as well and we had them.
"Swansea are a side which look as if they're going to score more goals this year, I've said that before, and they showed that again today."
Mirallas was making his second Premier League start and scored his first goal in the English top flight with a close-range header after Michel Vorm had saved his first effort and Moyes was encouraged by the Belgian's performance, hoping he can replicate the fine form he showed at Olympiakos last season.
He continued: "It was a great goal, he had another one which hit the underside of the bar, and I think one before that which the goalkeeper spilled and we didn't get on the end of - I thought he looked as if he was a threat to score a goal.
"If he follows up the goals he scores in Greece, we'll be delighted."
Everton's first goal was scored in controversial circumstances with Fellaini appearing to handle the ball into Anichebe's path before the Nigerian swept home but the 49-year-old backed the officials having missed the incident, admitting he had not spotted the foul himself.
"If the referee got it wrong then he got it wrong," Moyes said. "You have to say it if he did. I didn't see it from where I was, I needed an eagle eye, the way it's been spotted."