The 24-year-old completed a switch to United last summer worth up to £90m with add-ons, despite his agent hinting that he was on the brink of extending his Goodison Park contract.
Moshiri insists that he did all he possibly could to persuade Lukaku to remain on Merseyside, but the Belgium international - who scored 87 goals in 166 appearances for the Toffees - was determined to move on.
"With Romelu I wasted two summers trying to keep him," he said at Everton's AGM. "I spoke to him, his agent, his mother. We tried to offer him a better offer than Chelsea. He wanted to play for Chelsea though - at that time. [Chairman] Bill Kenwright has been like a father to many players, but ultimately it's the agents they rely on.
"If I tell you what we offered him, you won't believe it, and we offered him an even better deal than Chelsea, whatever they offered we matched but he just didn't want to stay. 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.
"Ultimately we lost money. To buy Rom now would be £120m. The issue was his brain had gone. He was in LA 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."
Lukaku has had mixed success since arriving at United at the start of the campaign, scoring 15 goals in all but just five in his last 21 outings.