Liverpool moved seven points clear of second-placed Chelsea, with a game in hand, although Arsenal can climb to within six points when they host Ipswich on Friday.
But Dutch manager Slot, in his first season in charge since succeeding Jurgen Klopp, remains cautious about the prospect of bringing the Premier League title to Anfield for the first time since 2020.
"If you are in this game for a long time like the players and I am, then 20 games before the end you don't look at it as there are so many challenges ahead of you," he said after goals from Cody Gakpo, Curtis Jones and Mohamed Salah helped turn the tide following Jordan Ayew's early strike for Leicester.
"Injuries and a bit of bad luck can happen to any team, it is far too early to be already celebrating –- but it is nice for us to be where we are."
Slot added: "I don't think there was any easy win for us in any of these games; it could have been an easy win against Tottenham but we conceded two... that tells you how difficult it is to win even when you have all your players available.
"That is why we have to take it one game at a time. The league table is something of course we are aware of but we always understand how many games there are to go."
