A victory would have guaranteed the Spanish outfit a top-two finish in Group H and they looked likely to achieve that after taking a 29th-minute lead through Diego Perotti's free-kick, as well as doing almost all of the attacking.
However, they were hit by a sucker-punch in the 71st minute when Liberec midfielder David Pavelka was given free reign to run almost from box to box before beating Javi Varas and equalise.
The Andalusian side tried to respond and they almost snatched a last-gasp winner when Juan Cala hit the post, but the Czech side held out for a draw which sees them remain two points behind the group leaders.
Despite Thursday's disappointment, though, Sevillla should still qualify as they are five points clear of third-placed Freiburg with two rounds to go.
Unai Emery's men came into the match on the back of two demoralising league defeats, going down 7-3 at Real Madrid before losing 1-0 at home to struggling Celta Vigo, but they did not look short of confidence as they started in determined fashion.
Jose Antonio Reyes, Sebastian Cristoforo and Coke all tried their luck early on before Bryan Rabello saw his 23rd-minute effort tipped around the post by visiting goalkeeper Lukas Hroso.
Sevilla then won a free-kick in a dangerous position on the edge of the area after Raul Rusescu saw his darting run unceremoniously ended by Radoslav Kovac - and Perotti made the most of the opportunity as he curled his shot into the near top corner to make it 1-0.
The home side's attacking threat diminished for a while after that, but it was back in force at the start of the second half with Hroso being called on to deny Perotti, Rabello and Rusescu, who also saw another effort deflected wide.
Perotti then fired a good chance wide with only Hroso to beat as Sevilla sought to finish the game off.
However, from another Sevilla attack that broke down on the edge of the visiting side's area, Liberec suddenly broke away and drew level.
Pavelka picked up the ball around 30 yards out from his own goal and was allowed to progress, virtually unchallenged, all the way to the edge of the Sevilla area where he drilled a shot past the diving Varas.
Sevilla, UEFA Cup winners in 2006 and 2007, sought a winner in the closing stages and they almost got it deep into stoppage time only to see Cala's brave header come back off the post.