It was a night to forget for Barca, who went down 3-1 to Spanish and European champions Madrid in the first leg at Camp Nou on Sunday.
Cristiano Ronaldo was sent off with eight minutes remaining but Madrid still triumphed on enemy territory thanks to the four-time Ballon d'Or winner, Marco Asensio and an own goal from Gerard Pique.
Lionel Messi's 77th-minute penalty restored parity after Barca team-mate Pique turned the ball into his own net early in the second half, however, Madrid finished strongly to take control of the Super Cup.
Speaking to reporters post-match, Valverde said: "I don't have the feeling that we were as far away from [Real Madrid] as the scoreboard indicates.
"They scored three goals, but this was a game in which we played well and had chances.
"Reaching their danger zones isn't all that matters, as you also need to hit the target. I don't believe that we're lacking goalscoring ability, but they were more clinical.
"They caught us in a one-versus-one situation and then scored one wonder goal and then another to make it 3-1. It was an even game and they had a strong central midfield, which made playing inside difficult.
"Their second goal really hurt us. We congratulate them and we will try to improve for the next match."
Barca travel to Madrid for the return leg at the Santiago Bernabeu on Wednesday.
"We have a very unfavourable aggregate score and the opponent is the favourite," Valverde added. "Now we have to play a second leg and things are never over after one defeat, or after one victory.
"When you lose you want another game to come along quickly to try to put things right. We are a little bit taken aback, but we have time to recover our energy."
Barca got a glimpse into life without Neymar following his world-record move to French giants Paris Saint-Germain.
Philippe Coutinho and Ousmane Dembele have been tipped to help fill the void at Barca and Valverde said: "We are Barcelona and we want to have the best team. We have time [to sign] until August 31, but I want to evaluate what we already have inside the club."