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."
"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."
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."