The Toffees slipped behind early on thanks to a Theo Walcott effort, but drew level as Marouane Fellaini curled home.
Moyes’ team had strong appeals for a penalty turned down when Mikel Arteta clashed with Steven Pienaar, which left the Scot reeling after the game:
“It was a really difficult night for us with the officials,” he told SkySports.
“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.”
However, Moyes did praise the efforts of his team to come back and in particular the contribution made by Fellaini:
“I thought he (Fellaini) was fabulous tonight,
“But our whole team played well, as we had to do against Arsenal. Overall I was really pleased with how the players played.
“Arsenal played well, they had some moments but great credit to our lads after going a goal down after 50 seconds to get right back in it.
“I thought we deserved it when we scored, we were playing well, and it was a really good goal by Marouane.”