It has now won 30 of its previous 34 matches, the fastest any side has reached that number of wins in the history of the English Football League.
However, despite needing just nine more points from its four remaining games to surpass the record, Klopp insists he is not bothered about making history.
“It’s not important for me; I’m not interested in any of this but I want to win football games,” he said after the match.
“For sports people in general it might be important. We are champions and it could be softening but it is not — the boys go with everything.”
Salah, Mane, Firmino milestone
Liverpool certainly didn’t have it all its own way against Brighton, which fought back diligently after falling two goals behind within the first 10 minutes.
A goal from Leandro Trossard had given the hosts hope, but as Brighton pushed for an equalizer, Liverpool’s talisman Salah popped up with a deft header to put the game to rest.
The Egyptian now has 19 goals in the league this season and sits just three behind current top scorer Jamie Vardy.
Klopp has now seen his dynamic front trio of Salah, Sadio Mane and Roberto Firmino score 250 goals during his reign at the club — a total which is likely to be added to in the remaining games.
Salah leads the way with 94 goals, with Mane hitting 79 and Firmino with 77 in all competitions.
Liverpool host Burnley in its next Premier League match before two tricky ties against Arsenal and Chelsea. The Reds then face Newcastle in the final game of the season.