Moyes was in charge of the club for 11 years and secured six top-six finishes during his spell with the Toffees.
The club lost only seven matches in Moyes' final season, but goalscoring issues saw the club score only 55 times in a season where the manager felt the team could have achieved more.
"I was here for 11 and a half years, and I think by the time we finished, we had a great team. I think our style was as good as anyone," Moyes told Sky Sports.
"We were probably a centre-forward away from being contenders for the Premier League.
We had Mikel Arteta, Steven Pienaar, Leighton Baines, Seamus Coleman, Sylvain Distin, Phil Jagielka, you could go on with the players we had. It was a terrific team."
Everton proceeded to buy Romelu Lukaku shortly after Moyes' departure, and the Belgian's subsequent Manchester United departure signalled the start of major spending by the club.
Having watched from afar, Moyes has been less than convinced by the club's transfer decisions in recent seasons.
"I think it's good they've spent money but we signed fantastic players with a great spirit, we had a great ethos at the club and what the club stood for - I think they've gone off that, a little bit," Moyes said.
"I don't know who made all the signings over the past few years, was it the owner, the sporting director or coach? But I know when I was here it was me, and I was always supported by Bill Kenwright.
"There's a lot of players who have come in and I'm not sure I would put all of them down as Everton-type players. But, for example, Richarlison was a great player for Watford last season, and he's got a good chance of improving too.
"You've got to be hungry, with a desire and energy, but you've got to have that style about you where you can play. You're under pressure here. The crowd are demanding, but they also want to see you're committed."
Moyes recently revealed that he would be interested in the U.S. national team job after leaving West Ham in May.