Liverpool reluctant to release Sturridge for England friendly
He is now a doubt for England's contest with Brazil this week.
"He got a knock just before half-time on his thigh," said Rodgers. "He wanted to give it a go in the second half but I think he'll be a doubt for the [England] game on Wednesday.
"It's unfortunate because he was terrific today. His hold-up play, his movement, his pace. He was a real, real threat. His combination with Suarez and Downing and Henderson up front was outstanding."