The Reds finished in fourth place in the 2017-18 season behind Tottenham Hotspur, Manchester United and eventual league winners Manchester City, but were the second highest scorers with 84 goals.
Draws were a major problem for the Merseyside club, with their 12 stalemates across the campaign being the most of any top-six side that season.
"We have to be more consistent. We know that. More clinical. More aggressive in the right moments. We need to improve everything," said the Liverpool boss in a press conference.
"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.
"We need to want more and fight more. That must be our attitude."
Klopp's side will host West Ham United at Anfield in their opening league fixture on Sunday.