Question marks were raised over the Welshman's ability to succeed at the Britannia Stadium after he was appointed 14 months ago following his dismissal at Queens Park Rangers.
"Maybe people are now realising that he is a good manager after all," The Sentinel quotes Coates as saying.
"Mark himself is bound to be feeling a lot better and more confident about things after last season's success, and also for having a year in which to settle himself into a new club.
"But in saying that, we all know next season will not be easy, and I'm sure Mark would be the first to say that. You take nothing for granted in football."
Stoke finished ninth in the Premier League table last season.