Liverpool have made a strong start to the season, having lost only once in 14 games in all competitions, which has propelled them to the top of the Premier League table and to the quarterfinals of the League Cup.
"It's a really good moment and I know that everybody compares with the past, especially at Liverpool. Three years ago, 10, five, 25 years ago - but this team is new, we are new," Klopp told the club's website.
Liverpool are the second most successful club in English football, but have been unable to add to their 18 league titles since 1990.
"Our story started a few months ago so you cannot compare us with anyone else. You cannot carry the history on our backs, we should feel free for creating something in the near future," the German, who joined the club 13 months ago, added.
"If everybody wants to say 'We wait now for 20-something years for silverware' or whatever, we can say 'Okay, we (have) tried, actually, only since a year'. So that gives us the freedom to look in the future quite optimistically."
Liverpool's next match is a trip to 10th-placed Southampton on November 19.