However, despite twice losing out to their fierce rivals, Valverde has denied suggestions that last season's double winners will ease to another league crown.
The 53-year-old told reporters: "There are no invincible teams, if there is one certainty in sport then it is that every single team will lose on one given day.
"When you lose and have the feeling that your opponent has been better than you then you can only assess the technical side of the game. Psychologically we wanted to win but it wasn't to be and now we have to recover psychologically, but we are a good team and we will adapt."
Barcelona begin the new domestic schedule with a home fixture with Real Betis on Sunday evening.