Antoine Semenyo (penalty) and Daniel Jebbison struck for the Cherries' 2-0 win.
Moyes said afterwards: "Yeah, there were some positives. We were really shabby in our overall defending in the first half but we'd done some good things - it wasn't all doom and gloom in the first half. We were 1-0 down and just before half-time, giving a second goal away was terrible really, that was the poor part of it.
"Ili had a little bit of a half chance in the first half, but, to be truthful, in the first half we didn't make many opportunities at all. We just didn't seem to be able to make things into the final third work, whether it be a good cross, whether it be a final through pass, we couldn't make that work.
"But I thought the second half was much better - big energy and great credit to all the subs who came on. I thought they all had an impact on the game, they made a difference, which gave us a little bit of hope and gave us something to think that we could get back into the game. But on a day where you hit the post three times and have one kicked off the line, you just get that feeling that it's not quite your day. So that was the way it was. We're disappointed to be out of the Cup but ultimately we've got a big job to do."