Proposals for a new ground at Walton Hall Park were announced in September last year but, like previous attempts to move away from Goodison Park, progress has ground to a halt.
Elstone insists the onus for what he called a "regenerative project" which would bring huge financial benefit to the area could not exclusively be placed on the football club.
He criticised the council for dragging their heels but Liverpool mayor Joe Anderson hit back on Twitter while Everton's general meeting was still taking place, stating: "Re EFC, CEO comments at AGM that they are ready on stadium
I am looking forward to receiving their planning and financial proposals tomorrow."
Elstone, speaking in front of shareholders at Liverpool's Philharmonic Hall, said: "Unless we get partnership with local authority it is going to be hard to bring it to fruition.
"It is a challenging funding project
We are looking at a massive regenerative project which will generate cash, economic benefit and social benefit.
"This is about regeneration of north Liverpool
It's a big prize for Everton but an even bigger prize for the city.
"It is absolutely why Everton has adopted a partnership approach and that is why we have built a regeneration case but at the moment we don't have a true partnership.
"We need confirmation on the City Council's partnership for accessing the park and level of investment they are prepared to put in.
"The mayor has said the onus was on the club but it cannot be exclusively on the club.
"Everyone associated with the project has to believe it is a regenerative project and it is not an Everton project - and from my point of view I don't think the council see it that way.
"You would need to ask Joe why he does not believe in that partnership.
"We are asking them to invest in the project but are offering them something which would generate a profit on their lending.
"Probably the biggest risk is the failure to grasp the belief in a transformational opportunity which could be Walton Hall Park but the club cannot do it on its own.
"If the onus is on us to deliver it we can't do it in isolation."
There has been talk in recent weeks of potential investment in the form of a buyer for the club but nothing concrete has so far emerged and Elstone said they were not even considering that in their financial planning.
"We believe the new stadium could work in a funding sense in a true partnership," added the chief executive, who gave apologies for chairman Bill Kenwright who was absent through illness.
"New investment is not being factored into finding a model as we don't know if or when it will arise."
The club, which has seen proposals for new grounds at King's Dock and Kirkby fall by the wayside in the last 15 years, has also explored the possibility of renovating Goodison Park but that would be a last resort and highly unlikely.
"We have considered a new stadium on same footprint but it is not viable," Elstone said.
"Redevelopment is going to be really difficult other than to add another tier (of about 5,000 seats) to the Park End stand.
"If Walton Hall Park doesn't progress as we want then maybe it will become a viable opportunity."
In presenting the club's annual accounts, Elstone expressed his satisfaction at reducing the club's net debt by over £17million to £28.1million in 2013-14.
"Net debt at the end of May 2015 is 33 per cent down on what it was two years ago," he said.
"We believe our debt levels are manageable and under control
We have a much more friendly bank manager.
"We now have organisations offering to lend us money but we've not taken our eye off the ball in getting value for money."
Source : PA
Source: PA