Dries Mertens’ 82nd-minute penalty and Fernando Llorente’s injury-time finish settled the Group E opener at Stadio San Paolo.
The Reds came closest to scoring a minute prior to half-time through Roberto Firmino’s header as goalkeeper Adrian produced a string of excellent saves throughout the match.
Jürgen Klopp’s side will now look to respond in the competition when they welcome Salzburg to Anfield on October 2.
