The Seagulls had fought back from two goals behind to force a draw at Anfield in October but were unable to launch a similar comeback this time around.
Luis Diaz opened Liverpool’s account with a header that saw him receive a heavy blow from goalkeeper Robert Sanchez in the process.
However, the subsequent VAR review ruled there was no red card for the goalkeeper.
Mohamed Salah’s second-half penalty put the game beyond the hosts, as the Egyptian forward recorded 20 goals a season for the fourth time in his five years at the Merseyside club.
“[It was a] difficult game, good opponent, needed a few minutes to get into the game. From the moment when we got into the game, we controlled it in a really good way,” Klopp said.
“I don’t think you can deny Brighton constantly and completely because of the quality that they have, but we tried well and scored a wonderful goal in a really good situation, could have scored more, good chances from open play situations or from counter-attacking moments, so both.
“Second half started with a good situation for Brighton but then after that we controlled it again, scored a second goal, then in the last two minutes they had a chance that was big but Ali is a world-class goalie, and he should not have to show it in each game, but he showed it again.
“That’s good and that’s why we have a clean sheet.
“I think we deserved the three points and that’s actually all I’m interested in and I’m happy about most of the things.”
Diaz was fortunately able to get to his feet and continue on the field in the aftermath of the goal, but Klopp believes it highlighted problems with the review system.
“I haven’t seen it back but it’s a very good example of the issues with VAR. The phrase ‘clear and obvious’ is a real problem,” the Liverpool boss continued.
“Because the phrase ‘clear and obvious’ is not wrong or right – nobody should feel like overturning somebody if the VAR is the team of the refs and not somebody from outside who thinks he might embarrass the ref because it’s his decision…it would help as well.
“There’s a lot to do for us today, [a] great goal but in general there is a lot of space for improvement, for sure.”
Brighton’s poor run of form continued as they slipped to a fifth defeat in a row – and they were unable to add to their poor tally of one goal in their last five matches.
When asked about the incident between Sanchez and Diaz, Brighton manager Graham Potter said: “I haven’t seen it back, my view or feeling really – because it was so quick – was that it was a top action from Liverpool and it was a great pass and a great run that was just too good for us and we mistimed it and then when that happens it’s a foul.”
On the game itself, he added: “I thought we responded second half and started again, had a go, but the quality of the opponent is high, we find ourselves 2-0 down with the penalty.
“I don’t think there was so much in the game at that point, but then we have to respond and I thought we did.
“I thought we finished the game really strong, the boys gave everything – it’s just the opponent was better.”