Herrera completed a switch to Manchester United on a four-deal last month, after the Premier League club met his buy-out clause.
The 24-year-old was an influential member of a Bilbao side that qualified for the UEFA Champions League via a fourth-placed finish in La Liga, making 33 league appearances and scoring five goals.
Valverde was saddened by Herrera's departure, but the 50-year-old is expecting others who can play his position to stake their claim for a starting berth.
"It [losing Herrera] is disappointing," he said. "He is a player who has given us a lot.
"[But] there are players vying for his position and we expect them to do as well or even better. We wish him the best of luck.
"I wasn't expecting the sale of Ander. [These] are issues that can happen."
Valverde also accepts that there is pressure on his side to replicate the form that saw them secure European football when the new campaign begins.
"FInishing fourth generates high expectations," he added. "We accept it, but it will be a complicated season.
"It is a challenge for us. Our aim must be to fight for positions that give access to Europe."
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