The Frenchman scored both of the Blaugrana's first two goals in a fine individual performance, which Valverde was keen to praise.
"I have to recognise that it was an important day for him due to the injuries we had. He reacted perfectly," Valverde admitted.
"He dropped into the midfield to help and he made an impact. We know that if attacking players track back, we have a better chance of winning."
It was crucial for Griezmann and Barcelona to react following the defeat to Athletic Club at San Mames last weekend.
"For us it was fundamental to put the game in our favour; we were very good," the coach said.
"We conceded a goal in a one-off move which destabilised us. We equalised afterwards and in the second half, we turned it around.
"We are scoring goals with few chances; it's a question of persisting."