Daniel Sturridge put the visitors ahead in the 24th minute but they could not add to their lead and former Everton striker Victor Anichebe capitalised on Toure's mistake midway through the second half.
"Kolo is devastated; I said to him sometimes it is the price you pay when you try to play football," said Rodgers, whose side failed to re-establish their four-point lead in fourth place over Everton. "He shouldn't have received the ball in the first place [from goalkeeper Simon Mignolet]. But we are in the position we are because 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."
The Hawthorns was the venue for Rodgers' first match in charge last season and, on that day, he left a 3-0 loser but expectations have risen significantly since then and a draw for his side now represents two points dropped. Rodgers, however, refused to see it that way. "We dominated possession and looked dangerous with the ball and it was just one of those unfortunate things where we made a mistake and got punished," he said. "Hopefully in the future we'll see it as a point gained but I think it tells you everything about our expectancy. We came here [and lost] and lost at home last year but we've got four points out of six and for us to be disappointed with a point away from home shows the growth of the team."
Pepe Mel, the West Brom manager, on the other hand, was pleased with the way his side responded to going 1-0 down. "We forget the way in the first half," said the Spaniard.
"In the second half we had a high press with [Youssouf] Mulumbu and [Claudio] Yacob behind doing good work. The goal came from a high press and a bad pass."