One shareholder asked: "Have the Board thought about Everton leaving Liverpool and what that means to the supporters?"
"It will be a long-term error to move out of the city limits, he continued. "It will be a mistake to go to Kirkby."
Another asserted that "we will be putting up the white flag if we move to Kirkby. It will be a disaster and our fan base will be eroded," while a third said: "This is a bit radical. Why can't we move to south Liverpool? Surely that is an option."
Kenwright pleaded that "I do not want to be the guy who moves Everton away from Goodison Park. I would love to say here forever." He insisted, though, that "it is not an financial option for Everton to remain at Goodison Park."
"I have also been told by the council it is absolutely impossible to extend the footprint of the club.
"As a board we have to make decisions and when we have made a decision we will go to the supporters." CEO, Keith Wyness added: "We believe there is enough merit to examine the situation further and will continue to work hard with our partners."
The club followed the meeting with an official statement which read: "Everton Football Club have given their full commitment to investigating the feasibility of Kirkby becoming the home of their new stadium and will not explore any other possible sites at this time.
"The three parties will produce a joint business plan that considers all potential elements of the proposed development. This plan will then be reviewed to ensure that it represents the best way forward for all concerned including the local community.
"Everton, Tesco and Knowsley Council are fully committed to involving the community and local businesses in discussions over a potential development in the coming months."
Meanwhile, details of the club's accounts were confirmed at the AGM.
Everton's turnover for the last fiscal year was down by £1.9m from £60million to £58.1million.
Kenwright attempted to put a positive spin on the figures: "Our drop down from a final placing of fourth to 11th last term cost us in terms of lost prize money and television money (around £3.2m).
"So the fact that turnover has dropped by £1.9million, year on year, does represent a very strong result."
The club's pre-tax loss was £10.8m compared to a £23.5m profit the previous year but those figures were heavily skewed by the sale of Wayne Rooney to Manchester United for £20m. Everton's net debt stands at £21.8m.
The biggest factor in the club's losses this past year was the increase in wages, from £30m to £37m.