The Reds found themselves 3-0 up at the Amex Stadium shortly after half-time thanks to an Emre Can goal and a Roberto Firmino double.
But Glenn Murray’s 51st-minute penalty evoked memories of Liverpool’s remarkable 3-3 draw at the Ramon Sanchez Pizjuan on November 21, when Sevilla battled back from 3-0 down.
Ultimately, Philippe Coutinho and a Lewis Dunk own goal wrapped things up for Liverpool late on, but Klopp acknowledged that he did have concerns when Brighton pulled one back.
“I would be lying if I said I didn’t think ‘yeah…’ ,” Klopp said.
“When you have it one time, unfortunately you need a little bit to get completely rid of this feeling.
“It’s not that I thought it would happen 100 per cent. We were 2-0 up at half-time, made it 3-0 shortly after and usually that’s it, especially how we scored it as well.
“They had a big chance, then we make a counter-attack and score – boom. That’s really hard to cope with for the other team.
“Then they make it 3-1, and while it [the lead] was not really insecure, it’s not that I thought it could not happen, because a few weeks ago it happened.
“We needed this so we don’t have that [the Sevilla game] in our mind completely.”
Klopp was particularly impressed with the performance of two-goal Firmino, praising his effectiveness at “annoying” Brighton.
“Roberto scored twice, but what he did around these goals is what excites me the most, to be honest,” he said.
“In all the counter-attacks, pretty much, he won the ball. By being here, by being a little annoying, a little foot, a little toe, that for us is important. Then the ball is go.
“With all the rest around him, you need to get used to it. They [the Liverpool players] are all different and all good.
“For me, I really like these players. That’s why they are here.”