Crouch appeared to poke his finger in Olsson's eye during Albion's 2-1 Barclays Premier League victory at the Britannia Stadium, something missed by referee Anthony Taylor on the day but picked up by television cameras.
The Potters striker faced possible retrospective action, but after the FA consulted Taylor, it was decided Crouch had no case to answer. Coates was quoted in The Sentinel as saying: "It is the correct decision."
He added: "Peter is a good character who plays the game in the right way.
"People within the game know that.
"Nobody involved made a fuss about it and that's always a good sign."