Brad Jones deputised as the Reds climbed to sixth in the Barclays Premier League.
Rodgers said: "It was disappointing because we thought he would probably make it today.
"He had a tight calf in a fitness test this morning and unfortunately for him he didn't get through it. Hopefully by next week he'll be fine.
"Big credit to Brad Jones, who came in at the last minute. He equipped himself terrifically today and made a great stop, especially in the first half.
"We'll see how Pepe is next week."