Everton were never able to settle on the ball as Aidy White gave Leeds a fourth-minute lead and the excellent Rodolph Austin doubled it with 20 minutes left.
Sylvain Distin would reduce the deficit with a header but Everton had left themselves with too big a mountain to climb, something Moyes was quick to acknowledge.
"We were not very good in the first half, but we got better in the second, but not as good as we've been playing," he said.
"We started terribly, gave them the initiative and lost the game in the opening 20 minutes due to the way we started. We gave away a really poor first goal and left ourselves trying to get back into the game."
On whether or not his decision to rest some players was key, he added: "These boys are in the squad and have to be able to show they can come in and play. If you don't use them, what's the point in having them? The players want to play and be involved."