Leicester City full-back Ricardo Pereira will be out for up to six months after having surgery on a ruptured Achilles.
Both players had to be withdrawn during Sunday's friendly win against Sevilla.
"It's such a shame because a lot of our game idea over the summer was based around full-backs and him [Pereira] in particular," said Rodgers.
"He was looking so good. It's a massive blow to him. He had his operation last night [Thursday] and he'll recover now, get strong again and come back better, I'm sure.
"He'll be a big miss for us but we have to push on.