The Championship side released a statement late on Friday night announcing that McDermott had left the club by mutual consent after little more than a year in charge.
Shortly afterwards, Cellino told me: "We did not want to go on pushing, pushing each other, and we found a gentleman's way to part.
"Brian leaves the club on good terms, he is a gentleman."
The 57-year-old says he doesn't have anyone lined up to replace McDermott - but he insists the next manager will not be Benito Carbone, who is the club's new technical consultant.
"I have always said that Carbone will be in charge of the Under-21s next season and that doesn't change now," he said.
Cellino arrived in London on Friday, having spent the last week in Miami for his daughter's graduation.
He will return to Leeds this weekend, before the club's players and remaining coaching staff arrive for a pre-season meeting on Monday.