Antoine Griezmann joined Barcelona for £108million this summer, just 12 months after turning down a move to the Nou Camp.
The Frenchman made his much-anticipated debut for the Spanish champions on Friday night, as Barca began their season at Athletic Bilbao.
With Lionel Messi ruled out through injury, Griezmann started in a front three along with Luis Suarez and Ousmane Dembele.
However, after Suarez suffered an injury in the first half, he was brought off and replaced with Rafinha.
Barcelona were unable to make the breakthrough, however, and were punished late in the game.
With the tie destined for a draw, Barcelona conceded in the 89th minute as they suffered an opening day defeat.
Aritz Aduriz scored an incredible overhead kick in the dying minutes to earn a shock win for the hosts.
And after the game, Valverde insisted that Griezmann needs to do more, and needs to impose himself more on the game.
“If he lives close to the box he can finish, he moves well, but you have to dominate the game for that to happen,” he told a press conference.
“Putting him on the left we knew that he will look for goal, but we have a left-back and players who can take the game.
“(However) we expect a lot from all the players and he has to look to get in the game more.”
Valverde also discussed Messi’s injury, and hinted he was unhappy with the way his team coped without their star man up front.
“It’s true we’re used to playing in a way and Leo shines in a lot of situations because he beats a man or filters a pass through,” he continued.
“We’re not all like him and we have to learn to cope when he’s not there.
“It’s inevitable to miss him, but we need to do other things too.
“We have to transform possession into goal chances, that’s what counts.”