The Reds had bounced back from conceding early on to carve out a 2-1 lead over the Cherries through goals from Philippe Coutinho and Origi either side of half-time.
But, with three minutes of the 90 remaining, Joshua King was allowed to turn inside the box and fire home, earning a share of the spoils for Eddie Howe's team.
Origi admitted to feeling downbeat when reflecting on events at Anfield, but called for focus to quickly turn to the tests that lie ahead in the battle for Champions League qualification.
He told Liverpoolfc.com: "It was disappointing, we wanted to win this game.