Klopp has made four big money signings, adding goalkeeper Alisson, midfielders Naby Keita and Fabinho and winger Xherdan Shaqiri, giving supporters genuine optimism ahead of the new campaign.
But the German on Friday insisted they were still underdogs in the battle for the league crown, saying: “We are still Rocky Balboa and not Ivan Drago.
“We have to be more consistent. More clinical. More aggressive in the right moments. We need to improve everything.
“We have to be in a championship mode. We jump into the water and we dive until we don’t have oxygen anymore. That’s the plan.
“A lot of people think because of the transfer window we will (challenge more) — but that’s not how it is.”
Klopp accepts the pressure ahead of Sunday’s opening match against a much-changed West Ham United.
But he said his team would also need a change in luck if they are to catch last year’s runaway champions Manchester City.
“Someone gave me the unluckiest team article,” Klopp added.
He was referring to a study released this week which said Liverpool dropped the most points last season, 12, in matches affected by wrongly disallowed goals or incorrect decisions.
“Concerning the gap with Manchester City, but we had three points from them last season and they had three points from us. It’s about losing them in other games.”
Klopp however pointed out that there could be further departures from Anfield, with the transfer window still open for major leagues in Spain, France, Italy and Germany.
“The window is only one way closed. So, we cannot buy any more but we can sell not in the English Premier League. But it is clear things will happen,” he said.