Allardyce claims the club blundered by emailing the questionnaire to Goodison Park season-ticket holders and says chairman Bill Kenwright has said sorry.
One question asked for a rating, between 0 and 10, on how they agree with the statement: "I have a high level of trust in the current manager and coaching staff at Everton e.g. in making the right decisions to get the best out of the team."
But Allardyce said yesterday: “I think from my point of view and club's view it was a mistake.
“It's allowed you to write some beautiful headlines.
“The chairman spoke to me. He — obviously, like me — didn't think it was the right thing to do.
“The director of marketing and communications has clearly slipped up. Our department has not been asked, 'What do we think of this survey that was going out?' If you just come to the football department and say, 'We have a couple of questions here, what do you think?' Then we might have said, 'Not really. We don't think that's appropriate.'
“The managing director of marketing clearly is not a great understander of football and how football works, because he is into marketing, branding and market research. So he must have thought it was the right thing to do — but clearly everybody hasn't."
When asked what mark he would give himself, Allardyce joked: “P*** off! Eleven!"