Gorka Guruzeta struck twice, with Alvaro Djalo also scoring for Athletic, while Iago Aspas converted a Celta penalty as a temporary equaliser.
"I can't remember a week like this, where you have three LaLiga games and you win all three. It was a crucial week," Valverde said post-match.
"We went to Las Palmas a bit tight on points, we needed to win and we've picked up nine points that will help us start the Europa League in a good frame of mind.
"The distance between defeat and victory is not that big in a league as tight as this one. We work hard so that the small details fall on our side and it's working for us."
He added: "It's always good for the strikers to score because it gives them confidence - although we don't really mind who scores. Goals and points in the first division are worth a lot."