Mikel Jauregizar, Nico Williams (2), Maroan Sannadi, Oihan Sancet, Gorka Guruzeta and Inaki Williams struck for Athletic. Mamadou Sylla scored for Valladolid, which also had Stanko Juric sent off ten minutes after halftime.
"Being competitive is about achieving good numbers, not just at a collective level but individually as well," Valvered said at his post-match press conference.
"Obviously, the consequence of all that is that you win points. It's important that our players are scoring goals and that they are ambitious enough to score, create assists and accumulate chances.
"Delivering on pre-match predictions is always difficult. Ultimately, you have to win matches in the Primera División and that's difficult.
"We started the game well with a high tempo, got the opening goal and had chances. Things could have got difficult when their equaliser was ruled out and then we made it 2-0 straight after.
"We were hurting them as pushed higher up the pitch. With their sending off, it was easier and they suffered for the situation they were in."