"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
AC Milan, Marseille, Roma and West Ham were among the other sides to also book their place in Friday's quarter-final draw.
Liverpool remain on course to send Jurgen Klopp off with a quadruple.
Mohamed Salah has given Liverpool a major boost after the Egypt star travelled to Sparta Prague for Thursday's Europa League clash following his recent injury lay-off.
AC Milan, meanwhile, were drawn against French club Rennes.
A youthful Liverpool side lost 2-1 at Union Saint-Gilloise in their final Europa League group game on Thursday, while Villarreal snatched a place in the last 16 from Rennes with a dramatic victory in France.
"It just was a really bad game, oh my god. We started well, really well, and then didn't continue. I think even before they scored, we just lost the plot a little bit, we were everywhere and nowhere," Klopp told reporters.
Atalanta knocked out Portuguese side Sporting Lisbon in the previous round but have won just two of their last nine matches in all competitions.
Leverkusen head into Thursday's home first leg against West Ham in the Europa League quarter-finals unbeaten in 41 matches this season, with 36 wins and five draws.
Jurgen Klopp's Liverpool, who are still in contention to win a quadruple this season, will entertain Atalanta at Anfield on April 11 and go to Italy a week later for the return.
AC Milan, Marseille, Roma and West Ham were among the other sides to also book their place in Friday's quarter-final draw.
Liverpool remain on course to send Jurgen Klopp off with a quadruple.
Mohamed Salah has given Liverpool a major boost after the Egypt star travelled to Sparta Prague for Thursday's Europa League clash following his recent injury lay-off.
AC Milan, meanwhile, were drawn against French club Rennes.
A youthful Liverpool side lost 2-1 at Union Saint-Gilloise in their final Europa League group game on Thursday, while Villarreal snatched a place in the last 16 from Rennes with a dramatic victory in France.
Jurgen Klopp's side sealed top spot in Group E thanks to Gakpo's brace and goals from Luis Diaz and Mohamed Salah at Anfield.