The champions, who did not lose last season until their 37th game, fell to their first defeat of the campaign by conceding two goals in the space of two second-half minutes after Philippe Coutinho had given them the lead.
The Catalans are still joint top of the standings, though, locked on 13 points with Real Madrid after six games.
"When any team concedes two goals in a minute it's an accident, but it's obvious we have to improve. I say the same even after a victory, but we know that here defeats cause earthquakes," Valverde told a news conference ahead of Barca's game at home to Athletic Bilbao in La Liga on Saturday.
"Whenever Barca lose it's a free for all for criticism and I'm not going to point the finger at anyone. I want to build the best team possible to win. My team has an extraordinary attitude, but we all make mistakes, me and the players."
Barca will be without injured France defender Samuel Umtiti for the game against Athletic, where Valverde spent four years as coach before he took over at the Nou Camp in 2017.
Despite Umtiti's absence and the criticism Valverde has received in recent weeks for rotating his team, the coach said he is considering resting Gerard Pique for the visit of Athletic.
Pique gave the ball away in the build up to Leganes's second goal, although Valverde insisted he is not concerned by the centre back's form.
"It's a possibility because (Clement) Lenglet and (Thomas Vermaelen can play together. I'm not worried about the error, I'm far more concerned about how we conceded the first goal than a freak mistake," said the coach.
Barca were undone by Leganes's high pressing and Valverde is aware of the threat Athletic pose to his side with coach Eduardo Berizzo, who masterminded three wins out of six games against Barca when he was coach of Celta Vigo.
"One of the keys to winning the game will be overcoming that pressure, it's fundamental if we want to play our usual game," Valverde added.
"Athletic are a team that press you high for 90 minutes, we've known that for a long time and they do it very well.
"Everyone knows all about Berizzo and how his teams play, he is direct and wants to stop the opponent playing, he did it at Celta, Sevilla and he's now doing it with Athletic. His teams have personality, they always want the ball and they have great spirit."
(Reporting by Richard Martin; Editing by Christian Radnedge)
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