The Potters have won just one of their last nine Premier League games and some supporters have expressed their frustration towards Pulis.
However, Coates believes that the current Stoke squad is the best the club have had since winning promotion in 2008.
"We are clearly having a bad run and not playing well but I think these are fine margins," he told The Sentinel. "Our current squad is the best we've had and to me that represents progress.
"[Pulis] has been here seven years and I think fair-minded Stoke supporters would think they were seven good years. Our worst finish in the Premier League has been 14th.
"We would like to finish higher, but this is a highly-competitive game and we are playing in the toughest league in the world."
Stoke are currently 11th in the table with 33 points from 28 games.