The Dutchman has achieved an impressive nine wins in his first 10 games as Liverpool's head coach, the best start for any manager in the club's history.
But Slot, who took over from Juergen Klopp after the end of last season, once again said judgment on his Liverpool side would have to wait.
Asked about his record start, Slot told reporters it was satisfying “and it’s actually also quite special if you know - and you know - how many great managers Liverpool had”.
He added: “I also said last week that I hope they don’t only remember me in one, two, three, four, five years only for this.
“We are hoping to do more special things than this and it also says the luck I had that I inherited a very good squad and a very good staff to continue getting the results that Juergen had here as well.”
Saturday’s slightly nervy victory ensured the Reds go into the international break top of the Premier League.
Liverpool’s early fixture list has been relatively kind, though they face sterner tests after the break with Chelsea at home followed by trips to RB Leipzig and Arsenal.
They will likely have to manage without Alisson, whom Slot hailed as “the best goalkeeper in the world”, after he was forced off late on with an apparent hamstring injury.
Slot told reporters: “If a player walks off like he does that normally means that he’s not in the Brazil squad and I don’t expect him to be in the team in the first game we play afterwards, but we have to wait and see.”
But, Slot added, the performance of debutant Vitezslav Jaros - on the bench as number two Caoimhin Kelleher was ill - was encouraging.
“It is very pleasing to see that our third goalkeeper... that even our third goalkeeper can have an impact on our results,” he said.