Coming off their first Premier League loss of the season, Liverpool visit Wolves in a tough cup clash on Monday.
While Liverpool have made progress under Klopp, they are yet to win silverware, losing Champions League, Europa League and Carabao Cup finals.
But Klopp said perhaps not even the FA Cup would be enough, with the club still looking to end a 29-year wait for a league title.
"It is always when people talk to me about silverware it always looks like we have to get each little thing," he said.
"If we won the FA Cup then people would say that we didn't win the Premier League for so many years. We cannot change what other people think.
"We have to try our best in every game we play and so far, not only this season but especially this season, that's what the boys did – and that's what we will try again and again and again and we will see what happens.
"I would say we had the toughest draw together with Chelsea in the first round of the League Cup. I don't know all the others, but [other than] Bournemouth versus Brighton there is not a lot of all-Premier League ties.
"We have to think about the whole situation, not being like children and jumping always from one problem to the next problem – we have to consider all and that's what we will do."
Klopp is set to make numerous changes for the trip to Wolves, including giving Alberto Moreno a rare opportunity this season.
Liverpool have failed to progress beyond the fourth round of the FA Cup since Klopp took over in October 2015.