City's only win since Boxing Day came against Reading last month, and even their usually fearsome home form has begun to suffer.
None of last season's top four won at the Britannia, but already in 2013 Chelsea, Manchester City and West Ham have left victorious.
Pulis was forced to call for a "reality check" after that latest defeat, which came on the back of a 1-0 reverse at Fulham.
But Coates said: "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.
"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."