The 75-year-old has defended the club's manager following a run of dismal form, claiming that the Potters have recently been on the wrong side of "fine margins"
The Welshman has come in for criticism from certain sections of the Potters' support after leading his side to just one win in their last 12 games.
However, Coates has launched a staunch defence of the 55-year-old, claiming Stoke have deserved more points from recent outings.
"We are clearly having a bad run and not playing well but I think these are fine margins,” Coates told Sky Sports.
"We did enough in the second half at Fulham to get something out of the game and I didn't think we deserved to lose against West Ham.
"If your team is not doing well, your crowd gets restive. It's no different in Stoke than anywhere else."
Coates also underlined the quality which Pulis has added to the squad and called for supporters to be "fair-minded" in their assessments.
"Our current squad is the best we've had, and to me that represents progress. He (Pulis) has been here seven years and I think fair-minded Stoke supporters would think they were seven good years," he added.
"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."