The Spanish champions have made an underwhelming start to the new season with their displays lacking the flair and panache of recent seasons.
It has led to increased scrutiny on head coach Ernesto Valverde, and while a 2-1 win over Villarreal has eased the pressure slightly, the manner of it will keep the Barca coach in the spotlight.
France international Griezmann scored Barca's first goal in the victory at the Camp Nou, and believes they will hit top form soon.
"We are far from our best version," Griezmann said. "But with the matches to come everything will be better.
"You have to keep working. There are new players that have just arrived. We try to do our best in the group, in the field."
Griezmann joined Barcelona from Atletico Madrid in July and acknowledged there is a gap between the two clubs in terms of expectation.
"It's not Atletico, it's different," he added.
"I'm not too bad, right? Three goals so far. I can do better, yes. But I have to keep working."
Valverde used Griezmann in a wide position against Villarreal and feels the striker's versatility will be an asset going forward.
"We knew when he came that he can move in several positions in the front," Valverde said.
"He works, he gets involved in the game and we see him do well. And every day he is more integrated."