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.
As the home side poured forward in search of a second-half equaliser, they left themselves exposed at the back, Willian tapping into an empty net in injury time after being unselfishly picked out by former Liverpool man Fernando Torres.
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 said. "It was just really unfortunate that he slipped at a crucial moment.
"He was doing everything he possibly could today, 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 today because after that he kept getting on the football."
