The visiting Toffees rarely troubled City's goal at the Etihad Stadium, but nevertheless the boss was pleased with their display.
"The players have done a really good job today," Moyes told Sky Sports News.
"We wanted to still play and try and score ourselves but it wasn't to be.
"[The result] was harsh on our lads because some of them played 120 minutes during the week."
The loss has seen Everton drop to tenth in the Premier League table.