Potters' striker Crouch appeared to poke his finger in Olsson's eye during West Brom's 2-1 Premier League victory at the Britannia Stadium, something missed by referee Anthony Taylor on the day but picked up by television cameras.
England international Crouch faced possible retrospective action, but after the FA consulted Taylor it was decided the 30-year-old had no case to answer and Coates believes it was the right outcome.
"It is the correct decision,'' Coates told The Sentinel. "Peter is a good character who plays the game in the right way. People within the game know that.''
He added: "Nobody involved made a fuss about it and that's always a good sign.''
Crouch has been sent off five times in a career spanning 373 appearances, but only two were straight red cards.