"Since I came to this club I have always had things very difficult and I will not drop my guard now," said Higuain. "I've always worked to overcome and achieve my goals and this season will be no different.
"In my mind I am doing my best for Real, as always."
Asked if Real missed Cristiano Ronaldo in their defeat at Sevilla, Higuain added: "Cristiano is a very important player for us, but that's not to deny that the team does not suffer when he is not here.
"This is precisely why we have a wide range of quality staff. The problem was more the great opponent."