The Toffees fought back after Theo Waclott’s first-minute striker put the Gunners ahead with Marouane Fellaini equalizing just before the half-hour mark.
Moyes suggests that the officiating from referee Michael Oliver and his team left a lot to be desired and indicated that it may have been a different result for his team if things went Everton’s way.
"It was a really difficult night for us with the officials," he told Sky Sports. "We got very few decisions tonight.
"If you are going to win games, now and then you need a bit going for you. A lot of results hinge on what referees do and the decisions they make.
"If we were going to win it was going to be without any decisions from the officials going in Everton's favour that's for sure."