The Potters appear to have done enough to preserve their Premier League status for another year, with back-to-back victories taking them on to 40 points for the season.
They have, however, found the going tough this term and Pulis has seen his position called into question for the first time since guiding the club back to the top-flight.
Coates is reluctant to speculate on what the summer holds for the current boss at the Britannia Stadium, but concedes that the club have work to do if they are to bounce back stronger in 2013/14.
He said in the Sentinel: "We have had a very flat second half to the season and nobody is trying to hide that.
"You are always trying to learn from such things to try and improve."
On Stoke's recent return to form, he added: "I know it is not mathematically guaranteed, but we are obviously delighted to be in the position we are in after two good wins.
"I was very anxious and very nervous."