The Liverpool striker pulled up in England training last Friday and missed the 2-0 victory over Switzerland in which his replacement Danny Welbeck scored twice.
Sturridge now faces up to two weeks on the sidelines and if the prognosis is correct is set to miss the games against Aston Villa, West Ham United and Everton in the league, Ludogorets in the Champions League and Middlesbrough in the Capital One Cup.
“The only disappointment for us was Daniel Sturridge coming back injured as he had started the season very well,” the Liverpool manager told TalkSport.
“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.”
Sturridge is apparently used to having two days to recover after matches, England having played Norway on the Wednesday, and Rodgers said: “I think clubs work differently at times to international teams. It’s more the recovery strategy.
“When we look at our players here we look at them individually in terms of what their needs are. Fast players would have a second day recovery while other players can work on that day. When you are that type of player like Daniel Sturridge, Raheem Sterling and boys like Danny Welbeck you need to recover them.”