The 18-time champions of England have failed to finish first in the top flight since 1990, with Brendan Rodgers coming closest to ending that drought with a second-place finish in 2013-14.
Klopp, who was unveiled as Rodgers' replacement on Friday, believes major silverware is possible before 2019 - though he has pleaded for patience as he attempts to build a side capable of challenging.
"It's absolutely surreal. I woke up this morning and I was manager of Liverpool FC. But I don't care about things like that, things like the press. I'm a normal manager and I want to work with the players on the pitch," he said.
"It's not so important what people think when you come in - it's about what you think when you leave. Please give us time. If we want, this can be a really special day, if we're patient.
"This is a really difficult league, with opponents which are big, maybe bigger. We can be successful in a special Liverpool way but we have to wait.
"I don't want to say we have to wait 20 years, when I sit here in four years I think we will win one title in this time, I'm pretty sure. If not, on to the next one - maybe Switzerland."
Klopp enjoyed strong success with Borussia Dortmund, winning back-to-back Bundesliga titles in 2011 and 2012, but the 48-year-old is wary of comparing the two clubs too closely.
"It's hard to compare two clubs," he continued. "It's similar - nobody is satisfied. But we don't have a pre-season, we're in the middle of the season nearly. But it's not important.
"In Dortmund we did what we had to do. I believe in the potential of this team. Everything is there.
"The problem is you can be as good as you want but you have no influence on how good your opponent is. You have to bring them on to your level, and kill them."
Despite his strong reputation following his Dortmund success, Klopp has played down the notion of becoming a "legend" at the club in the mould of Kenny Dalglish or Bill Shankly.
"It's cool that you're all looking forward to the work for the next few months and years but it's not for me to think about this," he added.
"No one of these great managers said at his first press conference 'My target is to be a legend'. We have to work in the present."