The Brazilian came off the bench to hit the winner - his first appearance for Real for some weeks.
"We are going to fight until the end," said Kaka.
When asked how he would like to respond to his critics who in the past few days questioned whether he was really injured, Kaka said, "I know how things work in football. The best answer I can give is on the field.
"I would like to ask Madrid fans not to doubt by injury."