After being a goal down, Mbappe struck twice as Real won on Saturday night.
He told Real Madrid TV: “It was a very important and match because Villarreal are one of the best sides in LaLiga. After the match against Atlético, with extra time, it was very difficult but we had to win today. We had personality, desire to play and win. We fought and we’re coming home with the three points.
“Everyone saw the Atlético match. It was 120 minutes playing with a lot of aggression and emotion. We know why we are here, we have to respect the badge and keep fighting until the end. We had to give everything we have, that's what we did today and it was enough to win."
Mbappe has now broken the 30-goal barrier in his first season in Madrid, so surpassing Ronaldo Nazario and closing on Cristiano Ronaldo's record.
"They are legends who have defined an era. It’s important, but they are numbers. If I score more goals than Ronaldo and Cristiano, it doesn't mean I'm bigger, just that my first season is going better. The important thing is to help and win titles. Scoring goals is important, but even more so if we win the LaLiga, the Champions League and the Cup."