Bayern won the first-leg of their Champions League quarterfinal 2-1 at the Santiago Bernabeu. Luis Diaz and Harry Kane had Bayern 2-0 ahead before Kylian Mbappe pulled a goal back midway through the second-half.
Kompany, on his 100th game in charge and with his 40th birthday on Friday, said: "I try to separate out things like that and my imminent birthday. This isn't over. We won't be too euphoric and if someone's celebrating a birthday with important games to go... well, my birthday's not important at all. If my guys win the game next week, maybe I'll have that feeling of joy.
"We've been very respectful of Madrid at Bayern. We appreciate what kind of club it is, what kind of team it is. But then there is also what we are and what it means for our players to go and try and win there: 'OK, if we play against the best team in the competition it's a challenge for us to go and win again'."
Asked if Bayern should've scored more on the night, the Belgian added: "No, we are happy... any win at the Bernabéu is a good result. We can build on it and the next game is at home.
"They were incredibly dangerous at times - look at their quality - but we stayed dangerous, too. Now our objective is to go and win at home."