The powerful defender was quite pleased with his side's performance and has urged them to show more of the same in the upcoming weeks
The Santiago Bernabeu side bagged the full three points courtesy of goals from Karim Benzema and Cristiano Ronaldo, and Pepe is determined to build on Monday's victory and string together a series of wins.
"The most important thing is that we won the game. It was a difficult match, but we worked hard and showed that we're a solid team that's capable of winning things," the Portugal international was quoted as saying by Marca.
"The season has really started for us now. We have a number of important games coming up and we have to show the same focus that we displayed against Rayo.
"Rayo made life difficult for us with their good players, and we have to keep up our good work in the next few weeks."
Real Madrid resume Liga action at the weekend at home against Deportivo la Coruna.