The Potters have been in freefall in the last couple of months, winning just one of their last 13 matches.
Their poor run has left them 15th in the table on 34 points, just three points above the drop zone.
"I suspect 38 points will do it," Coates told thisisstaffordshire.co.uk. "But certainly a couple of wins and you are OK because 40 points will absolutely do it.
"It's up to us now to get enough points to stay in the Premier League. We've got as good a chance as anybody else and it's up to us to see it through because no-one does you any favours.
"When I look at the fixtures I believe there are points out there for us, but it's up to us to get going on a run."
Stoke face a trip to QPR next week and Coates said: "It is tremendously difficult for them now, but they still have a fighting chance and they are certainly not down.
"I thought they were extremely unlucky with 10 men against Wigan on Sunday. I can only assume Harry Redknapp must have run over a cat to get luck like that.
"We know our big problem, we are not scoring enough goals.
"And against Villa on Saturday we were beaten in the end by a fluke (by Matthew Lowton). A great goal but not one that would normally go in. It killed us off at a late stage when I thought we were good for a point or could even have won the game after equalising."