The Merseysiders had looked as though they were on their way to another victory and to cement their place in the top four after going ahead in the first half through Steven Naismith.
The second 45 minutes was a different matter though and the Royals fought back to leave Moyes lamenting the way Everton failed to take their chances and kill the game off.
"I'm probably as p***** off as I have ever been after that, it was incredible," he said.
"We didn't punish them. We always left the door slightly ajar for them to come in, and they did do.
"We gave away a couple of corner kicks and a free-kicks in the opening 10 minutes of the second-half, we encouraged pressure by giving the ball away a couple of times in our own half quite simply, and we didn't pass the ball as we had done in the first-half. We gave them encouragement.
"After a result, this is the most annoyed I've been, because it should have been the other way.
"But we couldn't do it, and you have to give Reading credit because they hung in there."