The Reds won the Champions League last season, but they have ambitions of winning everything the game has to offer in the coming season.
And Klopp wants that to start with the UEFA Super Cup against Chelsea on Friday.
He said the following to UEFA's official website about the message he is giving his players: "Stay greedy. That's very important - I have no doubt about that, but it's clear that we have to do that.
"After the final we had about four weeks where everybody was [patting us on the back] and it was brilliant wherever we went.
"It's just nice, but in a different world things like this can soften you and it can take the power out of you a bit. We are not like this, but it's a fact that it could happen, at least.
"We only have to do the same again, and with a couple of things we maybe didn't do too well, we have to do better. That's how it is."