The Reds head into the new campaign as second favourites behind the reigning champions after strengthening their squad on the back of last term's fourth-place finish.
Despite spending big on the likes of Alisson Becker, Fabinho, Naby Keita and Xherdan Shaqiri, however, Klopp envisages a tough season ahead in what is widely billed as the most competitive of Europe's major divisions.
"The league will be difficult," he told the Liverpool Echo. "It is not about judging our situation and thinking 'wow, really good'. We need to be ready each week, not only for a few games. That is our challenge.
"If we win a game, we win a game and then we must win the next game as well, not be celebrating like it's the greatest thing. I really believe our fans are spot on and know what the situation is about. The people around that trying to create stories, I am not interested in that.
"We have high expectations of ourselves but our situation has not changed. Why should it? I do not see that United has got weaker or City weaker. Tottenham have not sold a player and have stayed together. I think Arsenal and Chelsea will be stronger than last year. Everton obviously are pushing from behind. Wolves are not shy to spend money.
"When I speak about not having crazy expectations, if we keep the atmosphere within the club from last year we have a chance of a really big season and then we will see what happens."
Liverpool face Torino on Tuesday night in their final pre-season outing, before welcoming West Ham United to Anfield next weekend for their Premier League opener.