The 49-year-old was frustrated that his side were unable to take any points from the clash at San Mames
Iker Muniain struck in the closing stages to secure all three points for the home side and denied los Che the chance to move into the top four, with the boss left frustrated that they were not able to take more from the match.
“We lost a great opportunity to enter the Champions League places,” he told a press conference.
“Bilbao pushed us, but we saw that we could hurt them. We're not happy because we could have taken more."
The defeat caps a disappointing week for Valencia following their midweek Champions League exit at the hands of Paris Saint-Germain, but Valverde insists the team is performing well even though the results are not forthcoming.
"I'm satisfied with how we are, the team is doing well," the 49-year-old went on. "If the problem is a matter of winning, we are working on it.
"The hardest thing is to create opportunities, and we are doing that. I would rather lose like this, deserving to win, because it means that we're in a good way."