Bilbao's disappointing start to the league season continued with the home defeat, as Jhon Cordoba's 39th-minute strike proved the difference.
Bilbao finished fourth last season to qualify for the Champions League but the addition of European football appears to be taking its toll on the club, who have registered just one league win from four matches so far.
Valverde rotated his squad for Saturday's fixture, making six changes to the team that drew 0-0 with Shakhtar Donetsk on Wednesday, but insisted it was not the reason for their loss.
"We didn't make a good start to the game, we didn't have a good first half," Valverde said post-game.
"Our playing rhythm wasn't sufficiently good enough for a game at San Mames.
"Our opponents were just as we expected them to be, with strong players in attack. We showed uncertainty and their goal came from a mistake."
Valverde added: "When you make changes to the side or lose, you always reconsider what you've done.
"The team is what we have, I've made decisions and we lost because we weren't good enough. We lacked rhythm and didn't play well offensively."
Granada coach Joaquin Caparros - formerly of Bilbao - was understandably more pleased after his side moved level on points with second-placed Atletico Madrid.
Bilbao only lost two games at home during the 2013-14 La Liga campaign.
"Playing here is just as complicated as at places like the Bernabeu or Camp Nou. I'm really happy," he said.
"We've got a result at a very difficult ground, it's super difficult here, but we've got three points."