"We are obviously disappointed with the start we've made but Mark and the management team have our full support," Coates told Telegraph Sport.
"He is a very experienced manager and knows what it takes to get results in the Premier League.
"It's still very early in the season and while these results obviously can't go on forever, we're convinced that things will change."
Hughes was fined 8,000 pounds by the Football Association (FA) on Monday after he accepted a misconduct charge in relation to an incident during their 4-0 loss against Tottenham Hotspur on Sept 10.
Stoke host Hull City in the third round of the League Cup on Wednesday.
(Reporting by Nivedita Shankar in Bengaluru, editing by Nick Mulvenney)
