Rodgers has been heavily criticised by fans and pundits after Liverpool's disappointing start to the season and he had to endure more boos from the Anfield faithful after another lacklustre display that left them with two draws from their first two Group B matches.
Adam Lallana put Liverpool ahead in the fourth minute when he converted from a Divock Origi cutback. But Sion equalised in the 18th minute when Ebenezer Assifuah chested down and fired past Simon Mignolet.
"I thought the result was disappointing considering the number of chances we created," Rodgers told BT Sport. "We started well but we gave away a disappointing goal, and they got in and finished what was probably their only chance."