Real won 3-0 on Sunday, with Mbappe opening the scoring on the night.
He later told RMTV: "I started well, with rhythm with my teammates, in a different position. As I said the first day I arrived here, I can play in many different positions and I will play to give my best, it is the story of my career, I play on the right, in the centre, on the left... I want to play well and score a lot of goals.
"It's been a lot of good for me to train these past few weeks with the Castilla boys. It's been good for me to run with them, to train... you could see that today, I feel good physically."
Mbappé added: "I have a good relationship with Vini, with him and with all the Madrid players, we are ready to play many games together and win many titles. Valverde? He is very, very important, when we talk about players, people love to talk about those who are seen the most and we don't talk about him much, but I can say that he is a very important player for us."
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