The Spanish rivals were locked at 0-0 entering the latter stages, but Neymar struck a late brace to secure all the points for the home side.
Valverde took a swipe at Barca, however, hinting that their budget is unfair compared to that of his team.
"Neymar is a star in his country. He's a player who cost more than the entire Athletic budget," Valverde told Marca. "He has a special quality."
Bilbao have lost two of their first three league games this season.