Both teams exchanged goals in a thrilling 2-2 draw at the Reale Arena, with Griezmann scoring the visitors' first goal.
"Both teams had their moments and had chances," Griezmann said after the match.
"We drew and we were good, had chances.
"We tried to score a third, but it wasn't to be.
"Both teams created chances to score a third and win.
"The Real Sociedad coach made two changes and they helped them a lot. They had lots of attacking players.
"We now have to start thinking about El Clasico."
The Frenchman didn't celebrate after finding the net against the club where he became a star in Spain.
"I'm never going to celebrate [against Real Sociedad]," he said.
I scored goals at the old Anoeta. I have lots of respect for those that gave me everything."