The Reds progressed to the quarter-finals on penalties after a thrilling encounter at Anfield, with both sides finishing the ninety minutes level at 5-5.
Origi scored the Reds' fourth with an excellent finish from outside of the box before acrobatically converting Neco Williams' cross in injury time to equalise and take the tie to penalties.
The Belgian has popped up at crucial moments for the Reds, notably against Everton, Barcelona and Tottenham last season, although he says he "can't really explain" his knack of scoring important goals.
"I'd say I'm just grateful, I can't really explain," the Belgian said.
"It's just instinct and I'm just grateful these moments are there. I'm enjoying them.
"I think it was a very entertaining game for both sides, a lot goals for both sides and a lot of talents. I think today was about mentality and who wants it the most.
"With the staff that pushes us and the fans and our energy, I think we made a great mix. We had to wait until the end to take the win, but it was well worth it.
"In this club that's one of our values - we just never give up regardless of what happens.
"Today I'm just happy [for] the young guys. I was in that position once and seeing them play and enjoying the game, seeing the fans always pushing us regardless of what happens, I think it's just very special.
"I'm so happy they could show it to the world. We obviously see it in training that they have unbelievable talent. For them to show it, it will make them grow.
“They showed that they are ready. We have a great team in all aspects and the coach knows that he can count on us.”
The Reds are yet to find out their quarter-final opponents, with the draw set to take place at 8.45am on Thursday morning.