Roberto Firmino, who was criticised by ex-striker John Aldridge for his performance against Newcastle United, failed to make the most of an attack as he unleashed a long-range effort that went straight into the goalkeeper's hands.
Inside the first 15 minutes, neither side managed to create a meaningful chance at goal as both defences seemed solid, while that final touch was missing from both teams.
It was Sion, though, who came close to making the breakthrough as Carlitos showed decent movement to pick up the ball on the edge of the box, but his shot let him down as his miss-kick soared above the crossbar.
Minutes later, at the other end, Firmino had a good opportunity to score, but his shot lacked power as the ball went right into the arms of the goalkeeper.
Divock Origi, who scored a hat-trick against Southampton last week, tried to get involved for Liverpool when he shot from the edge of the box, but his effort went just wide of the post.
It became more of an open game as Sion also had chances to break the deadlock - one of which came from Reto Ziegler, who hit a volley from just outside of the area, but it missed the target.
It was end to end as Adam Lallana came close for the Reds by getting in a good position for a shot from the edge of the area, but it was a poor effort as the ball sailed into the stands.
Liverpool showed some impressive passing movement in the middle of the pitch and ended the first half on the front foot, but Jurgen Klopp's men were unable to make their chances count.