And the caretaker manager condemned the supporters who threw bottles after Emi Buendia’s goal.
More than 100 fans remained inside Goodison Park after the final whistle against Villa.
They unfurled a banner that read ‘Sack The Board’ and chanted similar songs. There were also calls for chairman Bill Kenwright to leave the club.
Speaking in his post-match press conference, Ferguson said: “Fans, for me, can protest and say what they want about the club because it’s their club.
“They have got a right. It’s their club.
“I know how sick I would be, I’m gutted as much as them.”
Bottles were thrown from some Everton fans after Emi Buendia’s match-winning goal in first-half stoppage-time.
Matty Cash and Lucas Digne both appeared to be hit during Villa’s celebrations.
A fan was subsequently arrested after being identified on CCTV.
Ferguson said that the actions were not on.
He said: “I never saw the bottles thrown, I never saw that incident.
“I’ve been told after it and that’s bang out of order. That’s not the way to do things, it’s totally wrong.”
An Everton statement said: “A club statement explained: “Several objects were thrown towards the pitch following Aston Villa’s goal at the end of the first half, with one missile appearing to strike two opposition players.
“Investigations in conjunction with the police are ongoing, and the club will issue bans to any fans identified throwing objects.”