The Scot secured six top-six finishes in his 11 years at Goodison before taking over from Sir Alex Ferguson at Manchester United in 2013.
Everton lost only seven times in Moyes’ final season, but they amassed 15 draws – the most in the division that season – while scoring only 55 goals left them 10 points outside the top four.
Moyes told Sky Sports a goalscoring striker could have turned them into title contenders.
He said: “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.
“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.”
Following Moyes’ departure, Everton signed Romelu Lukaku for £24m before he also left for Old Trafford, with the club pocketing around £36m in profit.
However, Moyes believes not all of the Toffees’ big spending has been as beneficial for the club – and questioned who had been behind a number of their high-profile signings.
He said: “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.
“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.”