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The Spanish champions are in an unlikely eighth position after five Liga games after the shock 2-0 defeat at promoted Granada left the all-star outfit on seven points, their worst league start in 25 years.
"In my job the only thing that counts is results and the coach is always in the firing line," said Valverde, who led the club to the Liga title in 2018 and 2019.
"In the past two seasons we were already ahead at this stage, but we have started poorly and we need to put that right," said the 55-year-old.
Barcelona have yet to win away from home this season and play seventh placed Villarreal at the Camp Nou Tuesday and at 10th placed Getafe at the weekend.
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"The media being what it is you can plunge into a crisis in three days, and we have the chance to get out of it in three days."
"This is football. We have two matches and I want six points, it's the only way to calm the situation."
Valverde said his French winger Ousmane Dembele would be returning from injury Tuesday, naming him in his squad after a month on the sidelines.
Five time Ballon d'Or winner Lionel Messi, Urugauyan centre-forward Luis Suarez and French World Cup winner Antoine Griezmann are all also available.
"Dembele can shake things up," said Valverde. "We know what he can do, its now up to him to prove it on the pitch."