Sturridge out for up to eight weeks
The England forward, who suffered the injury during training on Friday, has scored 11 goals in all competitions for Liverpool this season and has linked well up front with Luis Suarez in the Anfield attack.
Rodgers told Sky Sports before his team’s match at Hull: “Daniel is probably going to be out six to eight weeks.
“It was something we thought was never going to be as serious as that to be honest.
“He slipped over in training and we thought initially it was his toe. He got brought inside straight away and he was taken for a scan straight away and it showed he’d actually got a ligament strain.
“It’s a big blow for us because he’s been brilliant since he’s come in.”
three in midfield with the inclusion of Fausto Rossi as they looked to provide extra cover for the backline but they could do little to stop the dominant Xabi Alonso and Luka Modric.
Real peppered the goal early on without luck, Di Maria having several shots saved by Diego Marino while Benzema and Sergio Ramos missing opportunities.
They eventually turned their dominance into goals after 33 minutes when Marino could only parry a Di Maria shot into the path of Bale, who headed home.
Real struck again within three minutes when Bale’s cross found Benzema, who nodded in.
Bale grabbed his second goal just after the hour when Carlos Pena’s clearance fell to him, and Real’s world record signing scored his third late on, finishing off a Marcelo cross.
Earlier, Celta Vigo eased their relegation fears with a first home win of the season as they came from behind to beat Almeria 3-1. Fabian Orellana, Borja Oubina and Charles Dias scored for Celta after Suso put the visitors ahead.