Smith held a meeting with the Leeds board last week and emerged far from happy with what he heard.
He said: "I went in under the impression they were going to move heaven and earth to get me to stay. But it was a long way from being that and they told me I wouldn't get a new contract even if we stayed up. I was full of optimism when I went into that meeting, but it's clear they plan to try to sell the players."
Caretaker boss Eddie Gray said: "This is as bad a day as I have had, but over the season we weren't good enough. This is obviously a sad day for the club, but it doesn't mean it's the end of the club. The club will survive. There will still be a football club in our city."