The Belgium international was in a meeting in March at which he was scheduled to sign a new contract -- around the time his agent Mino Raiola claimed the deal was 99.9 percent done -- when the U-turn happened.
"His agent went to Finch Farm to sign the contract," Moshiri told Everton's AGM.
"Then somehow during the meeting, Romelu called his mother and said she was on a pilgrimage to Africa and had seen some sort of voodoo message that said he had to sign for Chelsea."
Iranian billionaire Moshiri, who has pumped £150 million of his own money into the club to clear debts, said the Toffees offered the striker an "unbelievable" amount of money to stay, understood to be £140,000 a week.
"The issue with Romelu was not financial. As long as I am major shareholder financial issues are irrelevant," he said.
"I wasted two summers to keep him: first summer with his agent, him and his family we managed to keep him.
"Last summer we offered him a better deal than Chelsea, whatever they offered we matched but he just didn't want to stay.
"If I tell you what we offered him you wouldn't believe it but they offered him a better deal."
Lukaku, who is big friends with Manchester United playmaker Paul Pogba, eventually moved to Old Trafford in July for an initial £75m after Jose Mourinho caught his former side napping over the transfer.
"I got close to Rom, I like the boy, he's a good boy, and I used all my charm to keep him and I flatly failed," Moshiri added.
"Ultimately we lost money. To buy Rom now would be £120m. The issue was his brain had gone. He was in L.A. [with Pogba] and he wouldn't come back.
"It happens. Alex Ferguson got another year out of [Cristiano] Ronaldo but then he was off. [Luis] Suarez had to bite a few players to get off."
Moshiri was similarly unsuccessful in trying to keep boyhood blue Ross Barkley, who moved to Chelsea last week after backing out of a £35m deal on deadline day in August.
"I didn't spend as much time to keep Ross as I did Rom," added Moshiri.
"When it got to the two years I met his agent and said 'We need to extend the contract.' He said 'You need to get Ronald Koeman' and we got Koeman.
"He then said [John] Stones was his friend and he should be allowed to leave and he left.
"We got into the last year [of his contract] and again we didn't want him to go.
"Bill miraculously got an offer for £35m for a player who was injured and then he changed his mind.
"Sam [Allardyce] spoke to him and he didn't want to stay."
Plans for the club's new stadium at Bramley-Moore Dock are progressing but so are costs with chairman Bill Kenwright stating the development, which the club hope to be playing in by 2022, would cost £500m.
"Half-a billion is the estimate. Half-a-billion is what we are dealing with," he said.