The 23-year-old Denmark international turned down the chance to be on the substitutes' bench for the home match against Bournemouth two weeks ago and is now training with the Under-21 squad.
"After that game, he said that he didn't want to be considered for any of the games going forwards," Black told reporters.
"I didn't have a choice apart from remove him. I don't want people who don't want to be at Aston Villa."
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Villa's 28-year stay in England's top flight ended following their 1-0 defeat at Manchester United on Saturday.
The former European champions' American owner Randy Lerner accepted blame for the situation in a statement released on Friday.
Directors David Bernstein and Mervyn King left Villa Park this week and forward Gabriel Agbonlahor was suspended after being photographed on a night out in London with what is alleged to be laughing gas on the day their relegation was confirmed.
Okore, born in Ivory Coast, has played eight times for Denmark and joined Villa in 2013.
(Reporting by Ed Osmond; Editing by Toby Davis)
