Fede Valverde and Vini Jr scored for a 2-0 win which was marred by Dani Carvajal's knee injury.
Bellingham told Real Madrid TV: "I'm very pleased with the reaction, the performance and the result after a bad week that hurt us as a team. What happened to Dani leaves a bad taste in our mouths and they're still doing tests on him. We hope it's as minor as possible and that he can return as soon as possible. He's a huge player for us and has a great personality. We're keeping our fingers crossed for him.
“Villarreal are a good team, they move the ball well and have players with great quality. But we started better, pressing more aggressively and were quick in transitions. We scored two incredible goals and had control of the game even when we didn't have the ball.
“We practised this morning with Fede. I come in short, he passes the ball through my legs and Fede shoots from outside the box. It's a thing that Francesco put into practice on set-pieces. Vini's goal was a moment of individual brilliance. We kept the ball very well, we drew them in to open up space and Vini scored a great goal.”
He added, “I'm feeling good, I'm not scoring but I'm enjoying myself more because I'm participating more in attacking plays. I'm enjoying the way I'm playing. I want to score again, but the important thing is that the team wins and I can contribute to that.”