Captain Jordan Henderson said Liverpool deserve to be playing Champions League football after the club booked their place in the group stage of this season's competition.
The Reds will be added to pot three of Thursday's group-stage draw after with a 6-3 aggregate victory over Hoffenheim.
Emre Can, Mohamed Salah and Roberto Firmino got the goals in Wednesday's 4-2 win at Anfield in the second leg of the playoff qualifier.
And afterwards Henderson said: "It was a brilliant night.
"We set the tempo and scored some good goals early on. We still can improve on the goals we conceded but overall we're delighted to be back in the Champions League, where Liverpool belong.
"We need to make sure we do ourselves justice. They are big nights for everyone and I'm delighted for the fans and the lads.
"We've proved we can play against big teams and do well. We'll play whoever we get.''
Liverpool boss Jurgen Klopp added: "It feels absolutely amazing.
"My team played a perfect first half an hour...but Hoffenheim never gave up. 3-0 is usually a real knock but they were here to enjoy the game.
"You cannot imagine how much intense pressure there was on the boys before this game. We tried to put it away of course and the boys did outstandingly good.
"We should be there [in the Champions League] and we are really excited about who we get. We're really looking forward to the draw tomorrow.
"But I've told the boys 'have a party.' For sure that's what we should do, really enjoy tonight at home, the performance of today.
"I love the attitude of this team because they really fight.''
The German was again unable to shed any light on the Philippe Coutinho situation, with Liverpool having rejected offers for the playmaker.
Klopp added on BT Sport: "There's nothing else to say. It's not that I don't want to talk, I just have nothing to say, that's how it is.''