After months of negotiations to try and keep Lukaku at Goodison Park, Everton finally decided to let the Belgian move on to pastures new with Manchester United last summer.
Barkley is another high-profile player allowed to leave, to Chelsea this month, but Moshiri told a shareholders' meeting he did not try as hard to keep the England midfielder as he did Lukaku.
"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."
He added: "I didn't spent as much time to keep Ross as I did Rom."