"I can't say more except that we didn't play well enough to win the game," he said afterwards.
"I thought the first goal was always going to be crucial, and Arsenal hadn't done enough to be in front of us, we probably hadn't done enough to be in front of them, but they got the vital first goal just before half time.
"And the killer blow was for us to concede a goal right after half time before we could mount any pressure, and it sort of killed the game."
Moyes explained that the first goal, scored by Sagna, was undoubtedly the turning point.
"I didn't think we played well," continued Moyes, "But I do think maybe if we'd maybe managed to get that first goal instead of them it could have made a big difference."
The Goodison chief did take positives from the way things improved after he changed things in the second half.
"I think we kept at it - we changed," he continued. "It didn't work at first, but it took five minutes or so for us to get sorted, and then we altered it again a little bit and we got a bit of pressure.
"We deservedly scored a goal, but we ended up missing two or three chances, and on another day - who knows? We might have got something out of it."