Jamie Carragher still believes Everton are the worst-run club in the country and said the hierarchy have "demonised the whole fanbase" in recent weeks.
Everton sacked manager Frank Lampard after less than a year in charge on Monday.
Lampard's dismissal follows Everton owner Farhad Moshiri attending his first match since October 2021 as the Toffees succumbed to defeat at West Ham - their third consecutive loss in the league.
"Nobody knows a football club better than their own supporters," Carragher said on Monday Night Football.
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"There were no banners against Frank Lampard, they were against Farhad Moshiri and the board. I have said Everton are the worst-run club in the country. That wasn't a flippant remark as an ex-Liverpool player, I'm saying it as an ex-Everton fan. When I made that comment, Everton got in touch with me and I admired it, being on the front foot to defend your club. But I didn't think I was wrong then and I'm not wrong now.
"Moshiri doesn't know what he's doing, but he's got a lot of money.
"The same sorts of players are getting brought in, managers are getting changed left, right and centre. Why does every Everton manager fail? Lampard, Champions League winning managers like Benitez and Ancelotti, Silva, Koeman has been around the world. So when a club fails, you have to look at the top. It's a mess.
"The big problem is also the divide between Moshiri, Bill Kenwright and Denise Barrett-Baxendale - everyone in the city knows it. What is the role of Kenwright and Barrett-Baxendale at the football club? It's not financial. The owner is not listening to them. He does his own thing. If they are there for expertise they are not getting listened to. So what is the point of them being there?"
Everton's board of directors were told not to attend Goodison Park for their last home game against Southampton because of a "real and credible threat to their safety and security", according to a statement released by the club.
Fans' groups staged protests against the board at the match, which ended in another defeat.
"I think someone from the Everton board should have been at that game - the statement the club put out was bang out of order," Carragher said.
"It felt like they demonised the whole fanbase. I'm not saying the threats were lies - who knows? There was nothing reported to the police. But they threw the whole fanbase under the bus and you don't do that, especially in Liverpool, where you back your own, whether that is family or the football club. Those supporters kept them up last season.
"Supporters are protesting and want the board out of the club - on the back of that statement I don't see how they can go back to Goodison Park. Lampard may have gone but the banners aren't going anywhere until those people have left the club. Until there is serious change there, they won't get the fans back onside."
Everton's next six fixtures
February 4 - Arsenal (H), kick-off 12.30pm
February 13 - Liverpool (A), live on Sky Sports, kick-off 8pm
February 18 - Leeds (H), kick-off 3pm
February 25 - Aston Villa (H), kick-off 3pm
March 4 - Nottingham Forest (A), kick-off time TBC
March 11 - Brentford (H), kick-off time TBC