Klopp told BT Sport after the game: "I do not have enough words it is amazing. It is 14 months of the hardest work and it feels amazing. I can't find another word.
"A big big big compliment to my team. They played a perfect opening half an hour. I asked them at half-time to remember the feeling they had at 3-0 and to put it away.
"But credit to Hoffenheim, they played football and continued to enjoy the game. They can score two goals because of their quality. We didn't think we were the favourites but everyone else did so we had the pressure but the boys did good."
Liverpool, along with Chelsea, Tottenham Hotspur, Manchester City and Manchester United, will discover their group-stage opponents when the Champions League draw is made on Thursday at 5pm BST.