But he was substituted in the second half after a challenge by Ramiro Funes Mori, which saw the defender sent off.
“When I came in, everybody who saw the pictures thought maybe it’s broken. It’s not,” said manager Jurgen Klopp.
“I went to Divock in the medical room and I saw him smiling. The ankle is twisted so we have to wait to see what happens to the ligaments.
“That’s how it is. I can’t say more.”
Everton’s Funes Mori appeared to stand on Origi’s ankle and the Reds striker had to be taken off on a stretcher.
Klopp said after the game: “I haven’t seen [the tackle] until now. I didn’t see the television pictures. It’s a big shadow on the game, to be honest.
“Usually if you tell me before the game we will win 4-0, I would feel different. But now we can talk about the game and this situation – we have to wait for a final assessment. It’s absolutely too early.”