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The 48-year-old German was appointed as Brendan Rodgers' successor on Thursday, signing a three-year deal worth £15m.
He takes over a side who are 10th in the Premier League with 12 points from eight games.
"I was never a guy for an easy way," Klopp told LFCTV. "This is the biggest challenge in football. It is the most interesting job in world football."
Klopp, who will be joined at Anfield by his former Borussia Dortmund assistants Zeljko Buvac and Peter Krawietz, continued: "I read in the papers it is a disaster, but we are only six points to the top position in the table.
"It is interesting that nobody is satisfied or patient. We have to think about what to change. That is my job.
"I know what I want. First I need to talk to the players to find a common way. We will find that and who wants to do what I propose.
"Whoever wants to do what I want can be a good friend of mine. And it is not so bad a thing to be a friend of mine."
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Rodgers led Liverpool to a second-place finish in 2014, but they managed only sixth last season.
Klopp, who won the Bundesliga twice and reached the 2013 Champions League final during his seven years at Dortmund, said: "I am here because I believe in the potential of the team.
"In this moment we are not the best team in the world, but who cares? We want to be the best team in the world in the future.
"There are problems, you need to solve them. We have good defenders, strikers and midfielders. The first game is at Tottenham [in the Premier League on 17 October]. We need to make a team for this game.
"You have to change from doubter to believer. We have to change our performance because nobody is satisfied at the moment."
During Rodgers' tenure, Liverpool operated what has become known as the 'transfer committee' - a six-member group responsible for identifying transfer targets, considering their merits and conducting negotiations.
Twenty-three players were signed on permanent deals during Rodgers' reign for a combined fee of nearly £292m, with Luis Suarez and Raheem Sterling sold, to Barcelona for £75m and Manchester City for £49m respectively.
It is understood that Klopp will operate in this existing system but the German pointed out that he would have a decisive role.
"It's enough for me to have the first and last word," Klopp later told a press conference.
"We only want to discuss really good players. I'm not a genius, I don't know more than the rest of the world. I need the other people to get perfect information. It's really easy to handle it."
It is 25 years since Liverpool last won the league - their 18th top-flight title - under Kenny Dalglish.
"Twenty-five years ago is a long time," said Klopp. "History is only the base for us; [we shouldn't] keep the history in our backpack all day.
"I want to see the first step next week and not always compare with other times. This is a great club with big potential. Everything is there. Let's try to start a new way.
"I ask, please give us time. If you are patient and are prepared to work, in a special Liverpool way we can be successful.
"If I am sitting here in four years, we will win one title [piece of silverware] in this time."
Klopp introduced a style of powerful, high-speed football during his time at Dortmund - a style he says he will continue at Anfield.
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"Winning is important, but so is how you win and how you play the game," he said. "I believe in a playing philosophy that is very emotional, very fast and very strong.
"Everybody knows me. I haven't changed in four months. [My style is] emotion inside, it's speed, it's a transition game. All the things that make football interesting for me I want to see on the pitch.
"I have said this phrase 'full-throttle' football. It will be this.
"But it's not the day for promising a certain style of football. Let's start to work, let's speak next week, let's start normal work."
There are a number of revered managers in Liverpool's history, such as Bill Shankly, Bob Paisley and Dalglish, who won 12 league titles between them.
However, Klopp, who described joining Liverpool as "one of the best moments of my life", said he was more focused on the work he has to do in the present than on whether he could join them as a Reds "legend".
"I don't compare myself with genius managers of Liverpool," he said. "It's cool that some of you, and the fans, are looking forward to the next few years and months, but none of these managers said 'my target is to be a legend'.
"This is a great club because of many, many great decisions in the past. Now we have to work in the present."
In Jose Mourinho's first press conference after joining Chelsea in 2004, he described himself as a "special one".
Reminded of this and asked to assess himself, Klopp responded: "I don't want to describe myself. I'm a totally normal guy, I'm the 'normal one'."
New Liverpool boss Jurgen Klopp has described the Anfield job as "the biggest challenge" in world football.