The Premier League side visit Roma in the second leg of their semi-final on Wednesday, holding a 5-2 aggregate lead.
Klopp said he never expected his team to be in the Champions League decider, where Real Madrid await if Liverpool progress, at the start of the season.
"We were not even qualified for the Champions League, we had to play a qualifier, and I don't know who else reached the semis having been a qualifier at the start.
"The boys really stepped up. They constantly saw the competition as an opportunity.
"If this team goes to the final it would be an outstanding achievement already. It is not the prize we want then because if you go to a final then of course you have to think a little bit bigger, but it would be something we could not have expected at the start of the season."
Liverpool have overcome the departure of Philippe Coutinho to Barcelona in January to close in on the Champions League final.
But Klopp warned his team they had achieved nothing yet, still also bidding to secure a top-four finish in the league.
"Losing a player like Phil in the winter is big on the outside and I can say what I think and we tried to do something to sort it, but the decisive thing is what the boys think in that moment," he said.
"They obviously missed him and they miss him still because he is a fantastic boy, but they stepped up and played football.
"There have been so many big, big developments this year and it is really good but still there is nothing in our hands – not the Champions League final or even Champions League qualification."