A first-half goal from Mohamed Salah was enough to seal the deal for the Reds in what was a toughly contest affair.
While it wasn't as routine as many might've expected against Chris Hughton's Seagulls, Liverpool now find themselves top of the Premier League, undefeated, and yet to concede a goal. Jurgen Klopp's men also extended their record of clean sheets at home in the Premier League and haven't conceded a goal at Anfield in the Premier League since February.
Speaking to reporters (via the club's official website) after the final whistle, Klopp reflected on the game as a whole and where his side need to improve after Saturday's result.
"It was clear we will not start slowly and in the end we will show our best," he said.
"In this moment of the season, we started pretty lively, did exactly the right things. In the moment the concentration level dropped a little bit, you could see a few really wrong decisions and that gave them the opportunity to use.
"That is how football is, I can’t remember a perfect football game – and today was not a perfect football game, but it was good enough."
The Liverpool boss commented on goalkeeper Loris Karius' now confirmed move to Besiktas, calling the German stopper 'fantastic'.
Klopp added: "We said goodbye yesterday. He is really looking forward to it, so that’s good. It’s good for him, I really think. Loris is a fantastic goalkeeper at a very good goalkeeper age."