Barcelona boss Ernesto Valverde was left to face up to the second major European embarrassment of his time in charge.
The Spanish champions blew a 4-1 first-leg lead to bow out at the quarter-finals against Roma last year.
“The most hurtful thing is to repeat it,” said Valverde, who may struggle to hold on to his job despite guiding Barca to two La Liga titles.
“When you have a collapse of this nature we will have a few horrible days ahead.”
His sides were left to rue not taking their chances in the first half after weathering Liverpool’s early burst.
Lionel Messi had seemingly turned the tie in the Catalans’ favour late in the first leg with a brilliant free-kick and his first effort was tipped over by Alisson Becker before the Brazilian denied his international teammate Philippe Coutinho.
Liverpool were seemingly dealt another injury blow as Andy Robertson was withdrawn at half-time, but he made way for Dutch international Wijnaldum with James Milner moving to left-back.
Wijnaldum’s impact was massive. He was picked out by Trent Alexander-Arnold’s low cross and drilled under Ter Stegen. And from Liverpool’s next attack, Xherdan Shaqiri picked out Wijnaldum to head home at the Kop end.
“Once again we showed that everything is possible in football,” said Wijnaldum.
“I was really angry at the manager that he put me on the bench but I had to do something to help the team when I came on.”
Valverde tried to restore some order as Coutinho, who cost £142 million ($186 million) when moving from Liverpool to Barcelona in January 2018, was replaced for the second time in the tie.
The change briefly had an impact, but Barca were inexplicably caught cold from a quick Alexander-Arnold corner 11 minutes from time that picked out Origi completely unmarked to fire high past Ter Stegen.
“A genius moment,” Klopp of Alexander-Arnold’s quick thinking. “I saw the ball flying in the net and had no idea who took the corner and who scored the goal.”