The Reds progressed as a 4-2 win over Hoffenheim in front of a partisan home crowd sealed  6-3 aggregate victory.
Klopp's side will discover who they face in the group stage when the draw is made on Thursday from 17:00 BST.
"We should be there in the Champions League and we are really excited about who we get," said the German.
Liverpool produced a stunning attacking display against their play-off opponents to reach the group stage for only the second time in the past eight seasons.
It also ensured five English sides will compete in the group stage for the first time.
The Reds, who will be placed in pot three, join Premier League rivals Chelsea, Tottenham, Manchester City and Manchester United in the draw.
None of the English teams can be drawn against each other as sides from the same country are kept separate, although one could face Scottish champions Celtic.
Liverpool could be drawn against holders Real Madrid or Italian champions Juventus from pot one, while pot two contains five-time European champions Barcelona, big-spending French side Paris St-Germain and Klopp's former team Borussia Dortmund.
"There will be a few nice and difficult opponents but no-one, with this atmosphere, wants to get us in the group stage," said Klopp.
"I'm really looking forward to the draw."
Klopp, 50, will return to Europe's leading club competition for the first time since leaving Dortmund in May 2015.
He replaced Brendan Rodgers at Anfield in October 2015, leading Liverpool to the Europa League final in his first season but failing to qualify for Europe for 2016-17.
However, the Reds finished fourth in the Premier League in his first full campaign last season, setting up the two-legged play-off with Hoffenheim.
Asked what reaching the group stage meant, he said: "It is 14 months of the hardest work and it feels amazing.
"The Champions League is a big influence on the transfer market, especially if you do it more often."
Klopp said he had "nothing else to say" about Philippe Coutinho's future amid reports Barcelona were preparing a fourth bid of £136m for the Brazil attacking midfielder.
Liverpool have repeatedly stressed 25-year-old Coutinho, who missed the game through illness, is not for sale.
Liverpool are a team nobody wants to play in the Champions League group stage because of the atmosphere created at Anfield, says manager Jurgen Klopp.