PSG, who won the trophy for the first time last year, earned a nail-biting 5-4 victory in the first leg when Bayern battled back from 5-2 down in the second half.
Kompany told a press conference there was a feeling among his players and Bayern fans that they were ready to book a spot in the competition's final.
"There is this feeling that together we will take the next steps," Kompany said.
"Few believed it at the start of the season that we would have a chance with the last home game to reach the Champions League final."
"Now we are here, we have experienced great moments, and the fans believe we will make it, and together we want to make this moment unforgettable."
The Bavarians, in Kompany's second season in charge, have secured the Bundesliga title and can clinch the domestic double with a win over VfB Stuttgart in the German Cup final on May 23rd.
The Belgian, however, refused to be rattled by the pressure to deliver on the big European stage in front of a home crowd.
"Total calmness, internal calmness," Kompany said when asked how he felt.
"Not just before this game, but I try not to have this feeling of the game playing a role too early."
"Do the routine calmly, find the right words for tomorrow and just search for the right last phrase for the team to influence that one per cent," he said.
"We want to win the match. We have ideas that we believe will help us do that. The most important thing is to win the game, and that is the priority," Kompany said.