After a tough first half against newly-promoted Ipswich, Liverpool put on a show following the break in the Portman Road sunshine, running out comfortable winners thanks to goals from Diogo Jota and Mohamed Salah.
Juergen Klopp's successor Slot is just the second Liverpool manager in the Premier League era to record a victory on his league debut, after Gerard Houllier in August 1998 in a joint-management role with Roy Evans.
"The first taste (of Premier League football) in the first half was maybe as expected because they were all on top of us, very aggressive. Second half was a joy to watch," Slot told TNT Sports.
"I think we needed to win the long balls through the air. That helped and gave us control. I don't think Ipswich could keep up with the tempo in the second half.
"In the second half the players were ready and then opened up and you could see we can play quite good football."
Salah's well-taken second goal took the Egyptian to nine goals in the opening rounds of Premier League seasons, more than anyone else.
A goal and an assist at Portman Road suggested the 32-year-old will again be pivotal to any hopes of a Liverpool title challenge, but Slot does not believe his new team will rely too heavily on the man third in the club's all-time scorers' list.
"I don't believe that much in one man, I believe in the team more than the individual," Slot added. "He can score his goals because of good runs, good assists.
"I think Mo also needs the team but we also have more creative individuals who can decide the game."