Sturridge, whose career has been blighted by a string of injuries over the last three seasons, scored Liverpool's third goal, but immediately pulled up and was substituted in the 87th minute.
"He hurt his thigh. He has really prepared well, really well, so I hope this is just a small injury and that he can play again soon," Liverpool manager Juergen Klopp told reporters.
"It's a shame and I hope it's nothing serious."
Sadio Mane and Mohamed Salah also scored for Liverpool, who open their Premier League campaign at Watford on Aug. 12.
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(Reporting by Toby Davis; Editing by Rory Carroll)
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