Rodgers has suggested that the national side could have handled the striker's fitness in a better way.
He said: "We're obviously disappointed because we feel it was an injury which could have been prevented.
"He has worked so hard over pre-season and looked very fit and strong in our last game against Tottenham."
Rodgers said that players with more pace need to be given more recovery time than others, and the Liverpool boss seems to believe that is something the 25-year-old striker has not received.
As a result, Sturridge will miss Saturday's encounter against Aston Villa as well as the Reds' return to the Champions League on Tuesday. He's also likely to miss the following weekend's trip to West Ham United and the League Cup tie against Middlesbrough, but could feature in the Merseyside derby against Everton on September 27.
Rodgers added what might have caused the injury, saying: "I think clubs work differently at times to international teams.
"Fast players would have a second day recovery while other players can work on that day.
"When you are that type of quick player like Daniel Sturridge, Raheem Sterling and boys like Danny Welbeck you need to recover them."
It's frustrating for Rodgers to lose his first choice striker at such an early stage of the season having worked hard to ensure he doesn't miss as many games as he did last term. He may have scored 24 goals last term but had several niggling injuries.
Given the importance that Sturridge also seems to have for England, both club and country may have to get together and work out an alternative training programme for him to ensure he returns to his club in the best possible shape.