The Belgian ended City's recent spot-kick woes by by scoring seven minutes from time at the Bernabeu Stadium to seal a dramatic 2-1 comeback win in the first leg of their last-16 tie.
Between Sergio Aguero, Gabriel Jesus and Ilkay Gundogan, City had missed five of their previous seven spot-kicks but De Bruyne held his nerve under fierce pressure to put City in sight of the quarter-finals.
"But I think at this level you are going to have a couple of storms and you are going to have to weather through it.
"The first half was 50-50, the second half I think we started really well but then we made a little mistake and then came 1-0.
"But the reaction was really good. Afterwards we showed we could create some chances here. I think in the end we deserved to score two goals. It was a good performance."
City's performance showed their players are capable of putting the club's off-field problems to one side to deliver on the biggest stage.
They will now hope to complete the job in the second leg at the Etihad Stadium in three weeks, but before that comes the small matter of the Carabao Cup final at Wembley.
City will take on Aston Villa on Sunday bidding to win the competition for a third year in succession and a fifth time in seven seasons.
De Bruyne said: "No matter what happens you have to go again. If we'd lost we would have to go again on Sunday but we want to win the League Cup like every cup. It's obviously very important for us."