The Reds will meet Los Blancos in the showpiece encounter in Kiev on May 26 and will seek to stop Zinedine Zidane's side from winning a third consecutive European Cup.
Firmino, who has scored 10 goals in the competition so far, insists that Liverpool must continue to remain focused but is adamant that Real will have a game on their hands.
"Of course we dreamed big, I dream big and our whole team had that dream," the Brazil international told UEFA.com.
"Sure, we've had to win matches, go step by step, and put in a lot of work to reach the final. Now that we are in the final we also must remain focused. We know there is an equally well qualified team on the other side.
"It will be a great final. We know about Real Madrid. They are always winning titles in the Champions League and in the Spanish league too. They are a great team.
"This is a final and a one-off game. They'll be up against, in Liverpool, a team and a club with a great pedigree. We are going to fight until the end."
Liverpool last won the Champions League in 2005, though they went on to reach the final again two years later.