Late goals struck by Nico O'Reilly and Mateo Kovacic earned the visitors a 2-0 win.
But Moyes insisted afterwards: "We did a lot of good things, but just didn't have enough to get us over the line,” he remarked. “The people we brought in didn't make a difference in the game when we needed it to happen.
“So, yes, (there are) little bits of disappointment in that. But overall, the players have been great, and I can't complain. We're disappointed to lose against Man City. It says a lot. And for 60 minutes, we've done well today, I thought.”
Plenty of Everton positives
On the team's run of form since his return, Moyes also told evertontv: “The positives are that we're in a really strong position, so we mustn't get carried away with one result.
“I think most people would have probably expected a defeat against Man City, but I think the way the team's been playing, the confidence they've got, the results we've had – whether it be on the road or whether it be here at Goodison – it has given everybody the feeling that maybe we turn up and we beat Man City.
“We've drawn here against Liverpool; we've drawn here against Arsenal. So, we rightly felt we had a good chance today and I thought we did for long periods in the game.”