In recent years, Everton have often gotten off to slow start before finishing the campaign strongly, but Moyes is pleased to have won their first game of the season.
"I'm really pleased because we performed ever so well," said Moyes.
"We've often started the season slowly but just because we've won one game doesn't mean we've had a good start - as it would not have been a bad start had we lost.
"The only time we had a really good start here we ended in the Champions League places. I don't know if that's possible but it would be nice for us not to be playing catch up."
Next up for Everton is a trip to Aston Villa on Saturday.