The Reds have made an impressive start to the new season, scoring a remarkable 24 goals in eight matches in all competitions, but Klopp insists that nothing has been accomplished yet.
During his appearance on Sky Sports' Monday Night Football, he said: "I don't like standing here with all these numbers and saying 'brilliant, brilliant'.
"It is as good as it should be. We are a good football side, but we have to improve – not only in [defending] set pieces, but in a lot of things.
"We have done well, but Swansea (on the weekend) is the next challenge and it's a big challenge.
"Everybody feels good and that's good, it's better that we are all optimistic, but nothing has happened really.
"Football is a nice and simple game on good days, but on other days you can't find a solution and that's what makes it interesting."