Erling Haaland struck twice to earn the points for the hosts on Saturday.
Afterwards, Moyes reflected on evertontv: "I’m pleased with how we played. We were a bit disappointed when we lost the first goal. It was only 1-0 but to give them a second goal quickly was a killer for us.
"But there are a lot of good things we could talk about and what we've done well. We've come here and given them a bit of a game. Maybe we'd like to do better, but we're only growing at the moment and we're still trying to get better.
"We missed a couple of big chances in the first half, which might have altered things the way we were playing. We needed any opportunities we got to go in or to certainly get us something more positive than we did. So, look, no real problems with the performance overall – most of it. We've done a pretty good job."
Moyes also said: "I want to give the away support something to show, I want them to go to the games having hope and some faith that we're going to get results. Some of the results we had at Brighton and Crystal Palace was great, the celebrations we had. So I want to do that again.
"We weren't able to do it today but it certainly wasn't for the lack of effort or the lack of us trying to find ways of beating Man City. Ultimately their quality, their ability, their centre forward's got to finish things off and one or two players they've got as well make a big difference."