Adam Lallana fired the Reds in front after just five minutes at Anfield, before goals from Dmitri Payet and Michail Antonio reversed the advantage in the visitor's favour before half-time.
Origi - filling in for the injured Philippe Coutinho - then fired his sixth goal of the season as he took advantage of a Darren Randolph mistake to restore parity almost immediately after the restart.
Jürgen Klopp's charges couldn't muster a winning goal, failing to win for the third time within their last four Premier League games, but Origi says Liverpool must bounce back when they travel to Middlesbrough on Wednesday night.
Belgian striker: We can't lose hope despite drawing
Origi told Liverpoolfc.com that the club are entering a "busy period" and said that it's "good" to "concentrate on the game", which he said they "want to win, for sure."
The striker declared that "the season is long" and that "anything can happen" in the Premier League, insisting that they "don't lose hope" and must use the defeat "to come back stronger."
"I'm sure we will," Origi continued, insisting that "the most important thing" is that the squad "cool down" and "evaluate the game with the staff" in order to learn their lessons.
The Belgium international said that "there are points" that Liverpool "have to work on" but believes that they "just have to use the experience to come back stronger."
He admitted: "We are all disappointed. We wanted to win. They were in front and we came back, but maybe it was a little bit too late.
"In the end, we showed that we wanted to win and we missed a couple of chances, but next time I think we have to focus more and choose our moments to press and maybe luck will be on our side."
The more I play, the better I feel says Origi
Despite the frustrations of only taking a point against the Hammers, Origi scored his fourth goal in as many games in all competitions.
On maintaing his fine run of goalscoring form, the 21-year-old continued to tell the club's official website that "you always try to score" and that he feels that he is "growing in the game."
"As a player you need game time and the more I play, the more I feel better, but I still want to make steps," the Reds' No.27 said, insisting that "the most important thing" is "that you make steps but also win again."
Origi added that it helps to have "more game time" and it allows a player to "start learning" how to play alongside their teammates and vice versa, stating: "The more I play, the more I see their movements. So that's good."