Valverde spoke on Wednesday for the first time since Pique's goal celebrations in Sunday's draw and his disparaging post-match comments.
The coach stated: "All is well. It's already happened, so we have to take a step forward, otherwise we would never go forward.
"The controversy still surrounds football, because of a statement, a gesture ... All controversies can not be avoided. It's a bit boring to talk about all this. La Liga can do what it wants, I have nothing to say.
"This is a gesture we've known for a long time."