The Potters have won only one of their last nine Premier League games and some sections of fans have vented their frustration toward Pulis.
But Coates believes recent performances have not been as bad as results would indicate.
He told the Stoke Sentinel: "We are clearly having a bad run and not playing well but I think these are fine margins.
"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."
But Coates added: "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.
"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."
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