Barcelona have collected just seven points from their first five La Liga games which represents their worst start to a season for 25 years.
Furthermore, stretching back to last season, the champions have failed to win any of their last seven away games in all competitions.
Barcelona had Lionel Messi back in the league for the first time this season but even the five-time Ballon d’or winner could not conjure his usual magic when he was summoned from the bench in the second half.
Valverde has led Barcelona to two La Liga titles in his two seasons in charge, but his time at the Camp Nou has been shrouded in uncertainty at times, and he has moved swiftly to shoulder the responsibility for the champions’ poor form.
"In the end the actors are the players and the coach is responsible," Valverde told a post-match news conference.
"I feel responsible for what has happened. You can lose but when you lose you have to deserve to win - and today we have not deserved it.
"Away from home we are not reaping good results. When it happens in four games it is already a symptom that we are not too well.
"Today we have not been well. Away from home we are not playing good games. We are dominating but we do not translate it into goal situations. It is also true that the opponent is scoring the first goal."
"Granada deserve a lot of credit and we have to recognise it," the former Athletic Bilbao boss added.
"They have been intense, strong, they have troubled us a lot.
"The first goal has put the game in their hands and they hit us when they hurt us the most. They have made their game and that we have not played well is to their credit."
Barcelona are back in action against Villarreal at the Camp Nou in midweek.
