Both Liverpool and Sion went through from Group B after seeing out a goalless draw in Switzerland.
The Reds could face a number of big sides in the next round, including the likes of Borussia Dortmund, Fiorentina and Marseille.
The draw for the Round of 32 takes place on Monday at noon GMT.
“It’s never easy to go through, the games weren’t easy, but we did our job,” Origi, who played the full 90 minutes against Sion, told the club’s official website.
“Our objective was to go through and finish first because we are a big club and you have to be ambitious. Hopefully we’ll go far in the tournament and we’ll do everything to go far.
“I know there are some big teams. This is a big competition and we’re also a big team. We just have to be focused on ourselves and be well prepared.”
On finishing top of the group — and a potential return to Dortmund’s Westfalenstadion in the next round — Jurgen Klopp said, “We’ll see how important it is – there are a lot of very good teams in second place in the Europa League groups and good teams who have come in from the Champions League.
“Everybody who thought this tournament is not a first-class tournament will have to change their mind now – everyone will see it’s something like a mini Champions League. I am looking forward to the draw and we’ll see what happens.”