Jack Grealish struck midway through the second-half for the only goal of the evening, with Dewsbury-Hall named man-of-the-match for his performance.
Moyes said afterwards: "He played really well and I thought he made a difference in the second half.
"The game got a little bit stretched and a little bit transitional, with both teams having a bit of a go and I thought, 'My goodness if we're not careful this might suit them better here.'
"I think Bournemouth have got the highest physical stats in the Premier League so I knew that it might not suit us if it got that way because we didn't have that many changes we felt we were able to make as well.
"So, yeah, (Kiernan) did a great job, playing a little bit deeper, but I thought he still was the one who was probably going to try and open them up with a pass."
Moyes also said: "I think we've shown good solidity and I think we're going to have to do that at times.
"I wish we were scoring three and fours and making it look easier and we could be a little bit more open but we're having to shuffle things.
"Jimmy Garner went back to right-back again tonight because of injuries and I thought he was great against Antoine Semenyo for long periods of the game; the same with big Jake (O'Brien) at centre half – I thought he handled it really well.
"It took a lot of people to stand up. Tim (Iroegbunam) did great, especially in the second half, Tim stood up. So I'm really pleased. They've stuck at it and we're going to have to keep doing that. There were lots of positives to take from it.
"Hopefully we can keep it going. We want to take it on now to Hill Dickinson at the weekend. We want to get back into good form at home, that's what we really need to do now."