Aritz Aduriz opened the scoring for Bilbao from the penalty spot in the sixth minute but Nolito equalised in the second half in the 1-1 draw.
It continued Bilbao's slow start to the La Liga season, with just one win in eight matches to sit 16th.
Valverde believes his side would have been worthy winners at the San Mames Barria.
"We wanted to win and this result hasn't done justice to what happened in the game," Valverde said.
"The team has been fine... we got our goal and could have scored the second on several occasions, but in one good attack, they've levelled the game."
Valverde lamented his team's wastefulness and said Bilbao should have held more than a one-goal advantage before Nolito's effort.
"Maybe if we'd have been a little more precise, we could have had a better advantage by that time," he said.
"Their goal took the wind out of our sails a little but there was no lack of effort from my players.
"Our morale took a knock and from there, we weren't getting getting forward or able to get the crosses in we wanted to."
