"We won the Carabao (League) Cup already but we are Liverpool, we are a world-class club, we have a world-class team, so it's difficult to define a season as absolutely perfectly successful if you win the Carabao Cup only.
"We know that. The decisive part is coming now, no problem at all.
"It's the first time ever a team fought for the title and was in three finals -- so there's a reason for it because it's really difficult and really intense. Being here is good, but the icing on the cake is still missing and we are working on that now."
Liverpool have not won the FA Cup for 16 years, since Steven Gerrard broke West Ham hearts in a thrilling 3-3 final that went to penalties.
Only James Milner and Alex Oxlade-Chamberlain have won the trophy among Klopp's squad -- both at other clubs -- and the new generation of Liverpool heroes are keen to make their mark.
Forward Sadio Mane said: "I've been asking the boys, 'When was the last time Liverpool won it?' I think it was a long time ago. Not only the players, I think all the fans around the world are very excited to win it again.
"We won the Premier League, Champions League, so winning the FA Cup will be massive for us, for everyone at the club as well and the fans."