The midfielder lost his footing on the Anfield turf in first-half stoppage time, allowing Demba Ba to race clear on goal and slide the ball under Simon Mignolet.
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Despite the error in what was a damaging defeat to Liverpool's title hopes, Rodgers refused to lay the blame on his skipper.
"I said at half-time that this a is a boy who's picked up this club so many times," he told the press. "It was just really unfortunate that he slipped at a crucial moment.
"He was doing everything he possibly could but there's certainly no blame because we're in the position that we're in because of him.
"He's been instrumental for us this season, it's just unfortunate that he's slipped over and it could have happened to anyone.
"This is a guy that's so strong mentally. He showed his courage [on Sunday] because, after that, he kept getting on the football."