The Toffees continue to ride high in the table but have won just one of their last seven games, a sequence which includes five draws.
Moyes said: "That was pretty hard to take.
"But they were always in the game while it was only 1-0, that is the nature of the Premier League.
"I thought we played well for 25-30 minutes. We started well and controlled the game.
"Norwich grew into the game, give them credit, they had one or two opportunities.
"I thought we had got through the spell and we probably looked more likely to make it 2-0 than for them to equalise.
"But they did and that was it. We came away with a point."