The striker picked up the problem in a training session two days after playing 89 minutes in the national team's 1-0 friendly win over Norway at Wembley, ruling him out of their opening Euro 2016 qualifier in Switzerland on Monday.
And Rodgers believes Sturridge should not have been training at all so soon after playing close to a full match.
"The only disappointment for us was Daniel Sturridge coming back injured as he had started the season very well," he 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.
"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."
The injury leaves Sturridge out of Saturday's clash with Aston Villa and Liverpool's UEFA Champions League opener against Ludogorets on Tuesday.
He is also facing a race against time to be fit for the Merseyside derby against Everton in a fortnight's time.
"He's one to two weeks away [from playing again]," added Rodgers.
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