The Reds had taken the lead at the Hawthorns, but a wayward pass from the Ivorian centre-back mid-way through the second-half allowed Victor Anichebe to net the leveller in a game of few chances.
Toure’s error prevented Rodgers’ side from closing the gap to third placed Chelsea to a single point, and now leaves them looking back nervously at bitter rivals Everton as they entertain table-topping Arsenal at Anfield next weekend.
However, the Northern Irishman refused to criticise his defender, and instead hailed the sort of bravery and character members of his backline have displayed this season:
“Defensively, we were very, very good,” he told Sky Sports.
“I’ll never criticise players for trying to play football but Kolo probably shouldn’t have received the ball under pressure and his pass was misplaced.
“But for me, it’s the bravest place on the field as we look to build our play from behind. That has won us many games this season.
“We like to build the game and construct play from behind and sometimes it will cost you and today was unfortunately one of those days.
“Kolo Toure has been brilliant since he’s been here. He’s been a real leader, an outstanding professional and, unfortunately, it was a mistake.”
Daniel Sturridge had given the travelling side the lead in the first 45 minutes after combining with Luis Suarez to poke home, before Anichebe – a former Everton player – rammed the ball past Simon Mignolet after Toure’s error.