Ten points from their opening five Premier League matches has them handily placed in sixth after a difficult start saw them go to Arsenal, Chelsea and Tottenham.
Goals - 19 in seven games in all competitions - have been flying in with 10 different scorers already but Klopp has cautioned about getting carried away.
“Nothing has happened until now. We’ve only played five league games plus two cup games,” said the German.
“We need to find stability and create solutions for each situation. We are still working on that.
“We need to be ready for each game. There’s no time to look for excuses. We want to perform. We have the biggest expectation from ourselves.
“We don’t think: ‘Ah, we’ve got it’. Football is quite a simple game but it’s difficult to win.
“It’s not about celebrating ourselves but it’s better to have an optimistic mood than for everything to be in doubt. It’s up to us to use that.
“That’s how it is in football. We have to be ready for the next game. It’s not about the past.”
For all the optimism floating around Anfield, the 2-0 defeat at Burnley is still difficult to swallow.
It was a match Klopp’s side, on the back of beating the Gunners at the Emirates Stadium, were expected to comfortably win against the Clarets - but it turned out to be anything but, despite them dominating in terms of possession and chances created.
Today sees the Reds back at Anfield for only the second time this season with another newly-promoted team in Hull to get past.
Klopp is confident his side have learned from that chastening experience at Turf Moor and he dismissed the suggestion these were the games a team with Liverpool’s aspirations should be sweeping aside.
“We should not care about the name of the opponent,” he added.
“We didn’t care about it before we played Chelsea, Tottenham, Arsenal - not the name, not the players - only focusing on the style of play, what we have to do, where are our opportunities, where is the space we can create.
“We don’t think ‘Okay, what’s the name? For them only 50 per cent of preparation time’. No. We are 100 per cent aware of the difficulties we can have in this game.
“It is not easier against Hull. Why should it be easier?
“When we can win against teams which people think are stronger than we are, why can’t a team which people think are weaker than us have the opportunity to win?
“I’m not saying Hull are a bus-parking team. You don’t win all these games five or six-nil.
“I would like to see everybody go with the right expectation for this game and not be disappointed if we miss a chance after 10 minutes.
“I think we all can improve, and by all I mean the coaches, manager, and the crowd because it is all about expectations.”
Midfielders Adam Lallana and Gini Wijnaldum are set to return, while Hull midfielder Jake Livermore returns to contention following suspension. New signings Ryan Mason, Markus Henriksen, David Marshall, Will Keane, James Weir and Dieumerci Mbokani all started in the midweek EFL Cup win at Stoke on Wednesday night and will be hoping to make their first league starts.