The Potters owner has admitted to being disappointed by a series of "very flat" performances in the second half of the season, but failed to comment on the manager
Pressure mounted on Pulis after a run of just one win in 14 top-flight games dragged the team towards the relegation zone, before back-to-back wins over QPR and Norwich saw the club hit the 40-point mark of supposed safety.
And when questioned on Stoke's displays of late, Coates admitted to being underwhelmed and remained coy on Pulis' position.
"We have had a very flat second half to the season and nobody is trying to hide that," Coates told The Staffordshire News. "You are always trying to learn from such things to try and improve."
Stoke's upturn in form has now seen the club look back towards the top half of the table as they eye a top-10 finish.
Each improved standing come the end of the season affords a club an extra £800,000 in prize money, and with the Potters once occupying eight place earlier in the campaign Coates is keen for as high a finish as possible.
"I was very anxious and very nervous," Coates continued. "I know it is not mathematically guaranteed, but we are obviously delighted to be in the position we are in after two good wins."
"We deserved to win both games and it was a great relief because we haven't been in that position for a long time, but that's football and this is a tough league. You only have to look at all the teams down there.
"But the season is far from over because we have three games left and want to finish as high as we can."