After a run of three defeats in four games, Higuain struck both goals in Real's crucial victory.
"It was a tough week with all the pointless criticism we'd heard. Today we demonstrated that we are fighting in this league. It's still depending on us. We are in the Champions League and the Copa is very difficult, but feasible. We have the team to win," said Higuain.
"Personally, I am very pleased. I am still not 100 per cent match-fit, but I'm getting there."