Origi, one of five changes to the starting line-up, netted a brace in the win over the Reds' local rivals and was joined on the scoresheet by Xherdan Shaqiri and Sadio Mane.
Jürgen Klopp's side set a new club record with their 32nd consecutive league game unbeaten, while maintaining the eight-point lead at the top of the Premier League.
"It's a special atmosphere, a special game. I think as a team we just enjoy it," Origi told Amazon Prime post-match.
"There were a lot of goals today and we showed that we really enjoyed to play for Liverpool.