Sturridge, 25, strained his thigh in a training session last Friday, forcing him to miss England's 2-0 win over Switzerland in their opening Euro 2016 qualifier on Monday. He is likely to be sidelined for around two weeks.
The training session took place around 36 hours after Sturridge had played for 89 minutes in England's 1-0 friendly win over Norway and Rodgers believes the player should have been given more time to recover.
"We're obviously disappointed because we feel it was an injury which could have been prevented," Rodgers told talkSPORT radio station.
"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 quick player like Daniel Sturridge, Raheem Sterling and boys like Danny Welbeck, you need to recover them.
"He (Sturridge) has worked so hard over pre-season and looked very fit and strong in our last game against Tottenham."
Sturridge's injury means he will miss Liverpool's game against Aston Villa on Saturday, in which new signing Mario Balotelli is expected to make his home debut.