The Toffees are sitting 16th in the Premier League after 15 matches, only securing three wins in that time, leaving them just three points above the relegation zone.
With a home clash against Chelsea up next on Sunday 22 December, Sean Dyche’s side could head into Christmas while in the dreaded dropzone, with fans majorly concerned now.
Speaking via The Rest is Football podcast [20 December], Moyes said: “Everton were really important to me during my 11-and-a-half years there. People rarely spend that long at any club nowadays.
“It’s been disappointing that Everton haven’t competed but I think they’ve got a bit more than other teams in the Premier League and they’ll be fine.
“With them moving to the new stadium next season, it is really important that they stay in the Premier League, to which Gary Lineker replied: “It really is massively important. It’s a great football club.”
Alan Shearer added: “I think they’ve got enough experience, knowing how to navigate it.”