After a difficult first half at the Amex that saw the Reds dominate possession but not trouble goalkeeper David Button, their fortunes changed after the break.
Their breakthrough came via a mazy run from Mohamed Salah who, after being brought down by Pascal Gross, picked himself up and converted the match-winning penalty.
Liverpool ended the game having registered just three shots on target, but speaking at his post-match press conference, Klopp was delighted with his side’s close-fought victory.
“Today was not a day for a massive result,” the manager explained.
“They defended like they defended because they knew one mistake from us and they’re back in the game. We won it and I’m absolutely happy about that.
“It was one of the most mature performances of the season. Today was not a bad day, but it was a difficult game for us.
“We played a lot of times against a 4-5-1, it’s really difficult. I’m really happy that the boys took the game like it is.”
Klopp also praised his players for how they avoided handing Brighton opportunities from set-pieces, saying “this kind of concentration level is difficult to keep; the boys did it.”
He detailed the decision behind including Trent Alexander-Arnold in his starting lineup despite an injury scare in the warmup, with the right-back given the green light by his medical staff.
And Fabinho‘s performance as a stand-in centre-back came in for plaudits, with Klopp hailing the Brazilian as “a brilliant player.”
“It was not one attack after another, we had the ball most of the time,” he said.
And interestingly, he singled out Roberto Firmino for praise for his organisational influence when Liverpool took the lead, with the No. 9’s importance clear.