Real were outclassed 3-1 by the Rossonero on Tuesday night.
Butragueno later said: "First of all, I would like to express my condolences to the families of the victims (of DANA). The support of the Bernabéu and the whole of Spain was essential. They are with them.
"The game, obviously a bad result, was not what we expected. We know that we have to be solid, but they took advantage of their chances. It was a very adverse result. Madrid always wants to win and it wasn't possible. The way out is to work very hard and move forward."
Asked about Kylian Mbappe's struggles, he continued: "But he has clear chances in every game. The fact that the striker has chances is a good sign, but he doesn't have that amount of luck that strikers need. He also had very clear chances against Barça. Sometimes these situations happen. He is a player of enormous quality and it is normal for him to score again."
Asked if Real must buy in January, El Vulture added: "We trust our players. We won the European Super Cup, the Champions League and La Liga recently. We are not in a good moment right now, we have to admit that. But we need unity and the balance that a champion team needs. We have to stay calm. When the situation is not ideal, we have to be united."