Without the guile and invention of midfielder James Maddison, who was absent due to a recurrence of a hip injury, Leicester struggled to create chances while there was little of their trademark intensity for much of the evening.
Rodgers will also point to other injuries to key players, including James Justin, Wesley Fofana and Dennis Praet, while Kelechi Iheanacho was suspended, but this was still a tame performance.
“Patience,” was the constant order throughout the night from Kasper Schmeichel, the Leicester captain and goalkeeper.
This was always going to be a tricky night against a well-drilled, resilient and physical outfit.
In the first 90 seconds Slavia did not touch the ball until goalkeeper Ondrej Kolar saved from Cengiz Under.
Kolar also needed to be alert in the 20th minute to prevent Peter Olayinka from turning the ball into his own net.
Further chances in the first-half failed to materialise and with Maddison absent, Harvey Barnes also started on the bench, with Rodgers possibly considering the Premier League game against Arsenal on Sunday.
Slavia grew into the game and Sima, the teenage attacking midfielder, almost punished a mistake by Caglar Soyuncu with a low half-volley which bounced just wide of the bottom corner.