The Reds looked to be in control at The Hawthorns before Toure passed the ball across the face of his own goal and straight to Victor Anichebe, who fired an effort into the bottom corner to secure a 1-1 draw for the Baggies.
"Kolo is devastated. I said to him sometimes it is the price you pay when you try to play football," Rodgers is quoted as saying by PA.
"I've said to the team we are in the position we are because over the last 18 months we have shown the courage and bravery to play football and part of that is to build the game from behind.
"For the first time this season we got punished for that. He is an experienced guy and he knows it was a mistake and he is devastated. There is no blame. He has misplaced a pass and unfortunately for us it has cost us two points."