I agree with you, and to achieve that, it is very difficult, there are teams that are very good that find it difficult to achieve that, because most of them or they do well in their leagues and badly in the UCL, or they do badly in the leagues but very well in the UCL, Madrid has been a clear example of such a thing, however we as fans know very well that Liverpool comes from very good team organization with KLOPP, so the new coach only works on that scheme and from there on he has been able to do things well, it is difficult to change everything from one moment to another, it is not that easy, in this case they are doing things very well and I like it.
If you look at Liverpool's games for the next 3 to 4 weeks, you can see that they have a match every 3 days and will play against very strong teams like Chelsea, Arsenal, Leipzig or Leverkusen. It's going to be a very tough few weeks for the players and now it will really show whether the new coach has what it takes to replace Jürgen Klopp or whether it's too much for him and the team.
We can't say Slot has been having a bad start coaching Liverpool, if we take a look at the Premier league table with them being at the first position on the table, losing just a game out of seven matches played and also checking how they've played few of their matches in the Champions league already, i think is enough to confirm his ability towards having a better performance in the coming games.
Liverpool are going to put up a show, despite the outstanding tough games scheduled for the following weeks, they can successfully make something out of it, no comparison with Klopp but Slot is going to have it to his best looking at what he has already started and focusing on where the team is heading.