The fit-again midfielder struck twice from the spot to help Real to a 3-0 win.
Kaka said: "Those two goals are good for my self-confidence, they are very important goals.
"I understand the fans (criticism towards him). I hope that with time and with important games I can win over the supporters again. I only ask they give me time.
"I need to work hard to enjoy football again. The only problem was with my knee, which limited me from playing all out. I have to work hard in this final stretch of the season. I hope to have fun playing football.
"I feel like I owe it to Real Madrid and the fact that I haven't fulfilled expectations bothers me."