"The players did me proud in the way they played, especially in the opening 15 or 20 minutes.
"We know the statistics will be about Man City's passes and possession, but the one that mattered was that we got two goals."
The Toffees scored two goals inside the first 20 minutes to put them in charge at Eastlands and held on for the win despite Victor Anichebe's sending off and Phil Jagielka's own goal.
"Tonight was probably the least amount of opportunities we've made [in a match this season]," Moyes admitted after the win which lifted his team to 14th place in the Premier League.
"In a way I was disappointed that we didn't get more of the ball, but Man City are an improving team and they showed that."
Moyes was full of praise for his scorers Tim Cahill and Leighton Baines, and was particularly impressed by the latter's fine strike on 19 minutes.
"It was a dream second goal, it really was, great movement, great run and a pass into the far corner [of the goal] with Bainsesy's right foot. He should do it more often."
Moyes admitted Anichibe's sending off in the 60th minute made life difficult, and he disputed the first yellow card shown to the striker.
"I thought the first booking was nothing - he's tried to close it down, he's sort of turned his back, a bit frightened that he was going to get hit with the ball in the face, and his momentum's taken him into the goalkeeper.
"I think the crowd's reaction got it. I've not seen the second yellow, but it made things really difficult for us.
"We were 2-0 up at the time and doing fine, it was hard to contain them but it was always going to be much harder when we went to 10 men."
Moyes added: "The resilience and competitiveness of the team were excellent.
"When we come up against the top teams we give them a good game. Man City played well at times tonight but we defended even better."
Source: BBC Sport
Source: BBC Sport