The Reds sealed a 4-2 win over Bundesliga outfit Hoffenheim at Anfield in the second leg of their playoff for a 6-3 aggregate victory.
Liverpool's result means that they have returned to the Champions League group stages for the first time since the 2014-15 campaign.
Klopp told BT Sport after the game: "We wanted a fast start and fulfilled our dream. It was fantastic.
"Playing Hoffenheim was the most difficult draw, alongside Napoli, we had two unbelievably hard games. We learned from the first game and adapted to a little change when they changed from five at the back to four at the back.
"We are really excited about the group stage, whoever we get. There will be a few nice and difficult opponents but no-one with this atmosphere wants to get us. I'm really looking forward to the draw. Now I've told the boys to party. Enjoy it!"
Klopp has overseen seven European games - including qualifiers - as Liverpool manager at Anfield, with the Reds winning each of the last six.