Hughes agreed a fresh deal at the Britannia Stadium on Friday, which will keep him at the club until 2019, having guided the club to their best Premier League finish of ninth last season.
Stoke sit 10th in the top flight going into their final eight games and, with Hughes on course for another impressive campaign, Coates says he shares his manager's confidence about the future.
"I've long held the view that the critical appointment at any football club is the football manager, if you get that right then you will always have a chance," he told the club's official website.
"As ever, we do want to get better and Mark has aspirations to get higher up the table and we want to support him in doing that.
"It's great to have him feel like he can achieve progression here and it’s nice to hear him say it, he is certainly someone who is confident in what he can and can't do.
"I am always cautious in football because things can easily go wrong, but we are really pleased with the progress we have made and we're delighted with Mark's attitude towards that."
Hughes, who took over from Tony Pulis prior to last season, has also introduced a more attractive style of play with the help of flair players such as Bojan Krkic and Victor Moses.
"We have certainly done very well by finishing in our highest position which gave us a lot of pleasure and satisfaction," Coates added.
"When you make a change, you think it will put you back initially because people have got to get used to working under a different approach.
"I think he was surprised by the squad he inherited and how good a group he got, which was a nice thing to hear him say.
"He's done very well and the players have bought into him and the new style of play which has been very pleasing, exciting and encouraging."
