The Toffees face City at the Etihad Stadium in the Premier League on Saturday having won seven of their last eight meetings and all of the last four.
Those statistics would appear to be a good omen for the Merseyside outfit, but Moyes is keen to play down their significance.
"If you mention it, I'll smile, because we don't have records like that against so many big teams, but it is just one of those things," Moyes said.
"I don't take it for granted and I'm not looking at it, because you could quite easily tell me that we have a terrible record against lots of teams.
"I would shrug that aside and I'll shrug this aside as well - although obviously, I'm going to try to continue it."
Moyes feels City are now a more tricky proposition than that which Everton twice overcame last season and genuine title contenders after their manager Roberto Mancini strengthened his squad with another major spending spree over the summer.
"Last year it was much tougher and I think this year it will be even tougher again," Moyes said.
"I think there is a real chance of them competing with Manchester United, Chelsea and some other teams at the top to win the league, although I would say that with what they have bought, you would expect it as well.
"If you spend that sort of money you would expect to be very close, and I think they will be.
"It is like going into a gun fight when I've got a knife, so I have to find a way of using that right."
One of the most surprising pieces of business City did during the transfer window was signing Owen Hargreaves, whose injury-blighted spell at their derby rivals United had been brought to an end with his release by the Red Devils earlier in the summer.
Hargreaves has certainly made an impression already, scoring on his debut for his new club on Wednesday before subsequently making headlines with his controversial comments about the medical treatment he received at United.
Recruiting the 30-year-old for Everton was something Moyes thought about but did not consider necessary.
"I think Owen Hargreaves was out there for quite a few people who were interested. Manchester City took him and good luck to them and him," Moyes said.
"I think it was asked about and that his name was put around, but at the time we had no need for central midfield players."
City - currently second in the league - have started the campaign well, but Everton go into Saturday's clash in fine form themselves, unbeaten in five matches in all competitions after their midweek Carling Cup victory over West Brom.
The extra-time winner came from an unlikely source in club captain Phil Neville, who had sat through the Toffees' previous two fixtures on the bench.
Moyes has stressed that Neville's on-field leadership qualities are still vital and that the 34-year-old will play the "majority" of games this season.
When asked if it was a struggle for Everton at times when Neville was not part of the first XI, Moyes said: "It is, because he is more than just a player.
"He is that leader and is inspirational in so many ways. He will play a load of games this year - maybe not all of them, but he will be a big, big part of what we do.
"He will play the majority, I have no doubt about that. He is someone we can rely on."
Someone else who has been out of action recently is Louis Saha.
The French striker - who has missed the Toffees' last four games and been working on his fitness - vented his frustration on Twitter last weekend at not being selected for the squad to face Wigan and his chances of featuring against City remain unclear.
Questioned as to whether or not Saha was back in the picture, Moyes said: "Maybe.
"He has trained for another week, so that will help his fitness.
"Overall, I have to look at him to see if he is fit enough to play, but also at the other players to see if they are doing well enough to keep their place before him.
"There is nobody guaranteed a starting spot here, or on the bench, unless I think they are capable of changing and helping the team."
Source: Team Talk
Source: Team Talk