The result sees Barca go nine points clear at the top of the table and 19 points ahead of Real Madrid.
"It's true that there is a lot of distance. We've only lost six points," said Valverde.
"The numbers are what they are and we are very happy. The beginnings are always complicated, but the team has responded. What we have to do is look only at ourselves. You can never stay as you are and you must grow.
"We want to keep winning. If we settle, we will lose things."
Valverde admits they managed to overcome La Real's pressing game.
"They are a good team and we had difficulties. When tiredness appeared, it benefited us. When the opponent squeezes you and you overcome the pressure line, you have room to run. We've broken the bad run of results that Barca had here."