The 28-year-old made his first La Liga appearance for Barca, who suffered a shock 1-0 defeat to Athletic Bilbao in their opening fixture on Friday.
A €120 million signing from Atletico Madrid, all eyes were on Griezmann, but he struggled to make an impact in absence of captain Lionel Messi, while Luis Suarez’s first-half injury left him isolated.
If he’s near the area, he is decisive and moves well, but you have to dominate the game for that to happen,” Valverde told reporters.
“Putting him on the left side, we know that you are going to focus on the goal, but we have a side and players that can hold the game.
“Of course, he is aware that we all expect a lot from many players and he has to look to get more into the game.”
Suarez left San Mames just after the half-hour mark due to an apparent calf injury away to Athletic.
The Uruguayan veteran had to be substituted moments after hitting the post, which would have given two-time reigning champions Barca the lead.
Valverde added: “He has a muscular problem and we have to wait for the tests. In the second half, when we were around Athletic’s area, we missed him.”
Barca eventually succumbed to Athletic, who triumphed thanks to veteran Aritz Aduriz’s stunning overhead kick in the 89th minute.
The 38-year-old made an immediate impact off the bench, meeting Ander Capa’s cross in sensational fashion to seal all three points.
“With Aduriz, any ball in the air is a danger and he got his goal,” former Athletic boss Valverde said.
“That move is dominant, and he’s scored similar goals. When I saw him line it up… I wasn’t surprised with the execution at all.”
Barcelona will have the chance to make amends in their second league match as they host Real Betis at Camp Nou on August 25.
While Athletic will be hoping to continue their early season momentum in a August 24 road trip to Getafe.