The Toffees led at half-time courtesy of a Steven Naismith strike, but Adam le Fondre scored twice in the second period to turn the game on its head and earn the Royals their first league win of the season.
"I'm as angry as I've ever been after a game," said Moyes. "I'm not angry with the officials - I'm angry with my team.
"We were outstanding in the first half, like we were against Fulham and against Sunderland. But we didn't punish them; we left the door ajar, and let them in. We were more generous with them, we gave them corners and free-kicks, gave the ball away in midfield.
"You have got to give Reading and Brian McDermott credit because they kept at it, but we encouraged them. We are not putting away the chances we are creating."
Everton dropped one place to fifth in the Premier League table following today's defeat.