Bayern earned a valuable advantage in the quarter-final tie with a 2-1 win at the Bernabeu in Tuesday's (07.04.26) first leg, but the coach has urged his team to remain wary of the threat posed by the Spanish giants.
Kompany told reporters: "It’s a good result, we’re halfway through the tie. We have to recover and stay focused.
"We’re happy with the result; it’s a win, and any win here is important. We can build on that… and we’ll be playing at home.
"It’s only natural that they create chances; they’re very dangerous, but so are we. We have every right to dream that we can win again."
Bayern will be favourites to progress to the last four but Kompany knows that Real's history of famous comebacks in Europe needs to be taken into consideration.
The Belgian manager said: "I think we’ve shown a great deal of respect for Madrid. We fully appreciate what a team they are.
"But we’re Bayern, and we know what it means to play at the Allianz Arena.
"If we’re up against the best team in the competition, beating them is a challenge in itself."
Bayern's veteran goalkeeper Manuel Neuer earned the man of the match award thanks to a number of excellent saves, and Kompany believes the keeper deserves to be considered among the all-time greats between the posts.
He said: "We might get into trouble with (Thibaut) Courtois (laughs), who I also like a lot. He’s one of the chosen few.
"He’s been doing it for ages and his performances remain outstanding. I see him every day and he continues to impress us."