Liverpool are top of the Premier League and this victory follows a 3-1 away success over another Italian side, AC Milan, in the opening round of Champions League fixtures to give Slot’s side six points from six.
They still have six more matches to come in the league phase, including home matches against German champions Bayer Leverkusen, managed by ex-Liverpool midfielder Xabi Alonso, and 15-time European champions Real Madrid.
But they have made a perfect start to the competition and are fifth in the 36-team table, already in a strong position to push for automatic qualification to the last 16.
In Klopp’s almost nine years at Anfield, he won the Champions League, reached two finals, two further quarter-finals and reached the final of the Europa League.
Dutchman Slot, who managed in this tournament last season with Feyenoord, had said earlier this week how much he was looking forward to sampling the famous Anfield atmosphere on European nights.
The reality lived up the hype, further buoyed by a large contingent from Bologna – relishing the chance to witness European competition for the first time since 1999-2000.
“I don’t hope the only thing people remember me for in one, two or three years – you never know how long I’ll be here – they only say, ‘That is the manager who only won eight of his nine games’,” said Slot.
“I’m hoping to do more special things than winning eight out of nine games.
“You will probably never reach perfection. You are always aiming for perfection but you will never reach this.”