Fulham looked determined to make amends for their sluggish start against Manchester City and came out of the blocks quickly against Klopp’s men, forcing Alisson into two saves in the opening 15 minutes.
The hosts were rewarded for their possession and attacking threat in the 25th minute when Bobby Decordova-Reid fired past the Liverpool goalkeeper for the opening goal of the game.
The midfielder had been played in by Ademola Lookman down the left and he took a touch before beating Alisson.
Amid a host of defensive injuries, Klopp was forced into making a change at half-time as center-back Joel Matip did not reappear after the break.
Takumi Minamino was brought on for the defender, with Jordan Henderson assuming a new role in the centre of Liverpool’s backline as the Reds looked to overturn their 1-0 deficit.