It did not get much better after a 3-1 first-leg loss for Barca, who were outplayed in first half as Madrid put the result beyond doubt via Marco Asensio and Karim Benzema.
The midweek defeat completed a tumultuous pre-season for Barca following the world-record departure of star forward Neymar, and Valverde — a replacement for Luis Enrique — said the Catalan giants must recover and find their balance in the absence of the Brazilian star, now playing for Paris Saint-Germain.
"There are no invincible teams — if there is a certainty in this sport, it's that we are going to lose eventually," Valverde said.
"What we need is to win, to be sure, to be accurate. We have no qualms in recognising the merits of the rival. Madrid played better than us, especially in the second game, not the first."
Valverde, whose team open their La Liga season at home to Real Betis on Sunday, added: "We have lost this title, it is true. At times, they have started better, especially our first-half start and our second have not been very good.
"We had chances to get in the game but we did not capitalise. We have been penalised in the losses. We have to recover soon in the psychological point of view because La Liga starts. The Super Cup is the end of pre-season, although it is a title that we wanted to win. We have to pull forward. We have no other choice."
"In this world everything is evidence, each one is tested to a certain extent and difficulties always come in," he continued.
"There have been things in the pre-season that can affect the balance that there was in the team and we have to work on it to find another balance to be able to play well and get results.
"That is the team's work. It is a difficult moment because in big teams this happens when you do not win."