Playing in a European knockout game for the first time in their history, Augsburg came closest to winning it by hitting the post late on, but ultimately were able to pick up a draw to take back to the home of the five-time champions of Europe next week.
The home side had a good sight of goal in the opening minutes of the match when Mamadou Sakho could only clear a cross as far as Raul Bobadilla on the edge of the box, but the striker, who scored a joint tournament-high six goals in the group stages, fired his volley into the ground and up over the crossbar.
Liverpool barely featured in the opening exchanges, but were gifted a clear chance of their own in the eighth minute when Roberto Firmino picked up a wayward pass, only to send a tame shot straight at Marwin Hitz.
Clear opportunities were few and far between for the vast majority of proceedings, though, and the visitors were limited to half-chances through Daniel Sturridge and Jordan Henderson which were comfortably dealt with by Augsburg.
The hosts fired a warning shot of their own when Dominik Kohr lashed a powerful strike past the post, and then created the best chance of the first half in the final minute of the 45 when they played their way out from the back, eventually sending Alexander Esswein through on goal, only for Simon Mignolet to thwart the attacker.
Philippe Coutinho poked the first chance of the second half wide of the near post after good build-up play from the visitors, and another slick move shortly afterwards ended with Sturridge failing to get enough on a low James Milner cross to turn Liverpool's clearest chance of the evening goalwards.
Sturridge curled another one into the arms of the keeper moments later as the match began to liven up, and Hitz was once again called upon to prevent the ball from creeping over the line after an unfortunate bounce had almost resulted in Paul Verhaegh turning it into his own net.
It was beginning to look as though it would take something special to provide an opening goal, and Alberto Moreno almost provided it with a powerful, swerving strike that bounced up awkwardly for Hitz, who just about dealt with it.
It was the hosts who came closest to winning it, though, with Kostas Stafylidis failing to control a difficult effort at the back post before Ji Dong-won collected Caiuby's knock-down and fired a half-volley against the outside of the post.
However, neither side could find a winner in the closing stages of the encounter as the tie remained all square at the halfway stage ahead of next week's second leg at Anfield.